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Advanced Control Techniques for Grid-Interactive Smart Inverters under
Asymmetrical Conditions
by
Masoud Mohammadalizadeh Shabestary
A thesis submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
in
Energy Systems
Department of Electrical and Computer Engineering
University of Alberta
© Masoud Mohammadalizadeh Shabestary, 2019
ii
Abstract
Grid-interactive smart inverters (GSIs) are becoming the main interface for
integrating modern power units, such as renewable energies, energy storage
systems, electric vehicles, distributed generation (DG) units, microgrids, and high-
voltage direct-current transmission systems into smart power grids. Their expected
high integration in future smart grids brings certain reliability and complexity
challenges. Tackling these challenges with advanced control techniques can
provide more efficient and optimal operation in future highly interconnected power
grids. Riding through abnormalities while supporting host grids by smart inverters
is one of these challenges which has attracted a lot of attention among system
operators, regulatory organizations, manufacturing companies, and academia. This
research project thus aims to present novel techniques in four stages for optimal and
more reliable operation of GSIs, utilized in different configurations, under
asymmetric grid conditions.
In the first stage, a comprehensive control scheme, with multiple objectives,
is proposed for the optimal operation of a single GSI under unbalanced grid
conditions. These optimal behaviors bring significant advantages to the emerging
GSIs, empowering them to be more fault resilient and smartly responsive to
abnormal grid conditions. They also provide noteworthy benefits to the host grid
such as improving its stability, delivering maximum ancillary services, avoiding
unnecessary outages, better complying with the grid interconnection codes, and
increasing overall efficiency, reliability, and profitability. In the second stage, this
iii
research proposes a regulation guideline for riding through asymmetric faults as
well as dynamic flexible support of the grid. To date, most of the available grid
codes only focus on the regulation of the DG operation under balanced faults due
to the complexity, lacking the proper remedies for more common unbalanced
conditions. Implementing in different test cases and using comparative analyses,
the proposed regulation guideline and its unique control technique are proven to be
very effective and superior to the state-of-the-art methods. They can thus be
adopted by the updated versions of grid codes for more efficient integration of large
GSIs and DG units. In the third stage, a novel voltage support scheme is proposed
with improved accuracy in regulating the phase voltages within the pre-set safety
limits, by (1) considering the zero-sequence voltage compensation, (2) considering
the output active power and being adaptive to complex grid impedance, (3)
augmenting the adjustable limited active power oscillation and the maximum active
power delivery strategies. This empowers large DG units to provide their maximum
asymmetric support to the grid without a negative impact on their performance. In
the last stage of the thesis, the proposed techniques are extended for multiple GSIs
structures: (1) parallel-operated grid-interactive inverters (e.g., in hybrid energy
sources) and (2) multiple distributed inverters (e.g., in multi-DG active distribution
networks).
The effectiveness of the proposed techniques is validated using simulation
and experimental results. The proposed techniques facilitate the effective
integration of renewable energy resources, via reliable GSIs, into smart power
grids.
iv
Preface
This thesis is an original work by Masoud Shabestary. As detailed in the following,
some chapters of this thesis have been published or submitted for publication as
scholarly articles in which Professor Yasser Abdel-Rady I. Mohamed was the
supervisory author and has contributed to concepts formation and the manuscript
composition.
Materials in Chapter 2 have been published as two articles:
• M. M. Shabestary, and Y. A. I. Mohamed, "An Analytical Method to
Obtain Maximum Allowable Grid Support by Using Grid-Connected
Converters," in IEEE Transactions on Sustainable Energy, vol. 7, no. 4,
pp. 1558-1571, Oct. 2016.
• M. M. Shabestary, and Y. A. I. Mohamed, "Analytical Expressions for
Multi-objective Optimization of Converter-Based DG Operation Under
Unbalanced Grid Conditions," in IEEE Transactions on Power
Electronics, vol. 32, no. 9, pp. 7284-7296, Sept. 2017.
A version of Chapter 3 has been published as
• M. M. Shabestary, and Y. A. I. Mohamed, "Asymmetrical Ride-Through
and Grid Support in Converter-Interfaced DG Units Under Unbalanced
Conditions," in IEEE Transactions on Industrial Electronics, vol. 66, no.
2, pp. 1130-1141, Feb. 2019.
A version of Chapter 4 has been published as
• M. M. Shabestary, and Y. A. I. Mohamed, "Advanced Voltage Support
and Active Power Flow Control in Grid-Connected Converters Under
Unbalanced Conditions," in IEEE Transactions on Power Electronics, vol.
33, no. 2, pp. 1855-1864, Feb. 2018.
v
A version of Chapter 5 has been submitted as
• M. M. Shabestary, and Y. A. I. Mohamed, "Maximum Asymmetrical
Support in Parallel-Operated Grid-Interactive Smart Inverters," IEEE
Transactions on Smart Grids, Jan 2019.
A version of Chapter 6 has been submitted as
• M. M. Shabestary, and Y. A. I. Mohamed, "Decentralized Maximum
Flexible Asymmetrical Support Tracking in Active Distribution Networks
with Multiple DG Units," IEEE Transactions on Smart Grids, Dec 2018.
vi
This thesis work is dedicated to my wife, who has been a constant source of
support and encouragement during the challenges of my graduate studies and life.
I am truly thankful for having you in my life.
This work is also dedicated to my parents, who have always inspired me and
whose good examples have taught me to work hard for the things I aspire to
achieve.
vii
Acknowledgment
I would like to express my sincere appreciation to Prof. Yasser Abdel-Rady I.
Mohamed for his great support and supervision during this research project. This
research and dissertation would not have been possible without his continuous
guidance.
Also, I would like to extend special thanks to my examining committee
members, Prof. Yasser A. I. Mohamed, Prof. Venkata Dinavahi, and Prof. Yunwei
(Ryan) Li for taking the time to review this thesis. I am also thankful to the faculty
and staff members in the Department of Electrical and Computer Engineering at the
University of Alberta who provided a pleasant working atmosphere for me during
the past four years.
viii
Table of Contents
ABSTRACT …………………………………………………………………………….II
PREFACE ……………………………………………………………………………IV
ACKNOWLEDGMENT …………………………………………………………………………...VII
LIST OF ACRONYMS …………………………………………………………………………...XII
LIST OF SYMBOLS …………………………………………………………………………..XIII
CHAPTER 1 INTRODUCTION ........................................................................................... 1
1.1 BACKGROUND............................................................................................................... 1
1.2 STATE-OF-THE-ART ...................................................................................................... 3
1.3 MOTIVATIONS AND OBJECTIVES ................................................................................... 5
1.4 THESIS OUTLINE ........................................................................................................... 7
1.5 SUMMARY OF THE KEY CONTRIBUTIONS .................................................................... 10
CHAPTER 2 MAXIMUM ASYMMETRIC SUPPORT (MAS) IN A GRID-INTERACTIVE
SMART INVERTER ……………………………………………………………………………11
2.1 INTRODUCTION ........................................................................................................... 11
2.2 SYSTEM DESCRIPTION................................................................................................. 12
2.3 PROPOSED MULTI-OBJECTIVELY OPTIMIZED CONTROL STRATEGIES ......................... 14
2.3.1 Minimum Oscillation on the Active and Reactive Powers ............................ 15
2.3.2 Minimum Fault Current (MFC) Strategy ...................................................... 16
2.3.3 Maximum Allowable Active and Reactive Powers Strategies ....................... 17
2.4 VOLTAGE SUPPORT STRATEGY ................................................................................... 18
2.5 MAXIMUM ASYMMETRIC SUPPORT (MAS) SCHEME .................................................. 20
2.6 SIMULATION RESULTS ................................................................................................ 21
2.6.2 Test Case A: Performance Evaluation of MOP and MOQ Strategies........... 22
2.6.3 Test Case B: Performance Evaluation of VSS-MAP Strategy ....................... 22
ix
2.7 EXPERIMENTAL RESULTS ............................................................................................ 23
2.7.2 Experimental Test Case A: MFC Strategy .................................................... 24
2.7.3 Experimental Test Case B: MAQ Strategy .................................................... 25
2.7.4 Experimental Test Case B: MAP Strategy .................................................... 27
2.8 CONCLUSION .............................................................................................................. 27
CHAPTER 3 ASYMMETRIC RIDE-THROUGH (ART) GUIDELINES ............................... 28
3.1 INTRODUCTION ........................................................................................................... 28
3.2 OVERVIEW OF LVRT CODES IN DIFFERENT COUNTRIES ........................................... 29
3.2.1 Reactive current injection (RCI) ................................................................... 30
3.2.2 Frequency Control and Active Power Restoration ...................................... 31
3.3 PROPOSED ASYMMETRIC RIDE-THROUGH (ART) GUIDELINES ................................... 32
3.4 OVERVIEW OF CONVENTIONAL VOLTAGE SUPPORT STRATEGIES UNDER UNBALANCED
CONDITIONS................................................................................................................ 36
3.4.1 Positive-Sequence Reactive Current Injection (PSRCI) ................................ 37
3.4.2 Voltage Support Based on the Maximum Allowable Reactive Power Delivery
(MARPD) …………………………………………………………………………………………38
3.4.3 Mixed Sequence Injection (MSI) ................................................................... 38
3.4.4 Positive-Negative Sequence Voltage Regulation (PNVR) ............................. 38
3.5 COMPLIANCE OF THE CONVENTIONAL VOLTAGE SUPPORT STRATEGIES WITH THE
PROPOSED ART GUIDELINES ..................................................................................... 40
3.6 PROPOSED ART-ADAPTIVE VOLTAGE SUPPORT ........................................................ 45
3.6.1 Determination of Dynamic Reference Values for Minimum and Maximum
Phase Voltage Magnitudes .................................................................................................... 46
3.6.2 Reactive Current Injection ............................................................................ 48
3.7 SIMULATION RESULTS ................................................................................................ 48
3.8 EXPERIMENTAL RESULTS ........................................................................................... 53
3.9 DISCUSSION ................................................................................................................ 56
3.10 CONCLUSION .............................................................................................................. 57
x
CHAPTER 4 ADVANCED ASYMMETRIC VOLTAGE REGULATION AND MAS SCHEME
IN A SINGLE GRID-INTERACTIVE SMART INVERTER ................................................................. 59
4.1 INTRODUCTION ........................................................................................................... 59
4.2 PROPOSED ZERO-SEQUENCE COMPENSATED ASYMMETRIC VOLTAGE REGULATION
(ZCVS) SCHEME ......................................................................................................... 60
4.3 PROPOSED COMPLEMENTARY STRATEGIES ................................................................. 63
4.3.1 ZCVS with LAPO Strategy ........................................................................... 63
4.3.2 ZCVS with MAPD Strategy ........................................................................... 64
4.4 SIMULATION RESULTS ................................................................................................ 67
4.4.2 Test Case A: Traditional VSS vs Proposed ZCVS Method ........................... 68
4.4.3 Test Case B: ZCVS with LAPO and MAPD strategies .................................. 69
4.4.4 Test Case C: ZCVS Method under Various X/R Ratios ................................. 73
4.5 EXPERIMENTAL RESULTS ............................................................................................ 75
4.6 CONCLUSION .............................................................................................................. 75
CHAPTER 5 PARALLEL MAS SCHEME IN MULTIPLE PARALLEL-OPERATED GRID-
INTERACTIVE SMART INVERTERS .............................................................................................. 76
5.1 INTRODUCTION ........................................................................................................... 76
5.2 PARALLEL-OPERATED INVERTERS .............................................................................. 77
5.3 SYSTEM DESCRIPTION................................................................................................. 79
5.4 PLANE OF NEGATIVE REACTIVE VS. POSITIVE REACTIVE (NRPR).............................. 82
5.4.1 Allowable Current Areas in NRPR Plane ..................................................... 83
5.4.1 Allowable Flexible Voltage Support Areas ................................................... 84
5.5 PROPOSED OPTIMIZED ASYMMETRIC SUPPORT BY PMAS .......................................... 86
5.5.1 Stage I: Obtaining NRPR Equations ............................................................. 86
5.5.1 Stage II: AFSA Boundary Curves.................................................................. 87
5.5.2 Stage III: Convolution of Boundary Curves .................................................. 90
5.5.3 Stage IV: Determination of the Optimal Values ............................................ 90
5.6 SIMULATION RESULTS ................................................................................................ 94
xi
5.7 CONCLUSION .............................................................................................................. 97
CHAPTER 6 DECENTRALIZED MAS SCHEME IN MULTIPLE DISTRIBUTED GRID-
INTERACTIVE SMART INVERTERS .............................................................................................. 98
6.1 INTRODUCTION ........................................................................................................... 98
6.2 MULTI-DG ACTIVE DISTRIBUTION NETWORK .......................................................... 100
6.3 PROPOSED DECENTRALIZED MAXIMUM FLEXIBLE ASYMMETRICAL SUPPORT
TRACKING SCHEME .................................................................................................. 102
6.4 IDENTIFIED CONSTRAINTS FOR MSPT METHOD ....................................................... 105
6.4.1 Active Power Oscillation Limit (POL) Constraint ...................................... 106
6.4.2 Peak-Current Limitation (PCL) Constraint ................................................ 108
6.4.3 Allowable Flexible Voltage Support Areas ................................................. 109
6.4.1 Simplified MSPT ......................................................................................... 110
6.5 PROPOSED STRATEGIES TO DETERMINE MAXIMUM SUPPORT POINTS BY DSPM...... 111
6.5.1 MSPT with Flexible Ratio between Positive- and Negative-Sequences (FRPN)
……………………………………………………………………………………….112
6.5.2 MSPT with Bounded Autonomous Moving Points (BAMP) Approach ........ 112
6.6 SIMULATION RESULTS .............................................................................................. 114
6.6.1 Test Case A: Conventional vs Proposed ..................................................... 114
6.6.2 Test Case B: Proposed Scheme under Severe Conditions ........................... 118
6.7 CONCLUSION ............................................................................................................ 120
CHAPTER 7 CONCLUSION AND FUTURE WORK ......................................................... 122
7.1 THESIS ACHIEVEMENTS ............................................................................................ 122
7.2 FUTURE WORKS ........................................................................................................ 124
7.3 EXPECTED SIGNIFICANCE ......................................................................................... 125
REFERENCES …………………………………………………………………………..126
xii
List of Acronyms
AC Alternating Current
ART Asymmetric Ride-Through
DC Direct Current
DG Distributed Generation
DMAS Decentralized MAS
DOS Duration of Support
GSI Grid-interactive Smart Inverter
HVDC High-Voltage Direct-Current
LVRT Low-Voltage Ride Through
MAS Maximum Asymmetric Support
MSI Mixed Sequence Injection
PCC Point of Common Coupling
PCL Peak Current Limitation
PLL Phase-Locked Loop
PMAS Parallel MAS
PNVR Positive- and Negative-Sequence Voltage Regulation
POL Power Oscillation Limit
RCI Reactive Current Injection
NRPR Negative Reactive vs. Positive Reactive
ZCVS Zero-sequence Compensated Voltage Support
xiii
List of Symbols
A. Superscripts
+ Positive sequence components
- Negative sequence components
* Variable reference value
~ Oscillatory terms
B. Subscripts
p Active Power Component
q Reactive Power Component
C. Variables and parameters
ig Grid currents
i1 Inverter currents
V Voltage at the PCC
P* Reference active power of inverter
Q* Reference reactive power of inverter
Vg Grid voltage
Cf Capacitance of the ac filter
Rg Equivalent grid resistance
Lg Equivalent grid inductance
X Equivalent grid reactance
ω0 Grid angular frequency.
Ki Integrator gain of the current controller compensator of inverter
Kp Proportional gain of the current controller compensator of inverter
Ki,PLL Integrator gain of the PLL
Kp,PLL Proportional gain of the PLL
1
Chapter 1
Introduction
1.1 Background
In the past decade, driven by the worldwide concerns about the harmful foot-prints
of the fossil fuels along with the economic and political concerns, integration of
renewable energy resources, such as wind turbines and photovoltaic arrays,
combined with energy storage systems, into power systems has attracted increasing
attention as a vital solution. In 2015, the International Energy Agency has reported
that the energy sector contributes to almost two-thirds of all anthropogenic
greenhouse gas emission due to the use of fossil fuels [1]. Thanks to development
in power electronic technologies, large integration of renewable energies has been
possible by utilizing popular voltage source converters in various applications.
According to German and Danish Energy Agencies, the share of renewable energy
will be increased to almost 35% by 2020 in these countries, and the long-term goal
is to achieve 80% and 100% renewable energy share in the electricity sector,
respectively, in Germany [2] and Denmark [3] by 2050. Some other indicators that
show the rapid evolution in energy systems are more than 400 microgrid projects [4]
and more than 70 large high-voltage direct-current (HVDC) projects worldwide [5].
Thus, the power electronic converters play a more crucial role than ever before in
smooth transition from conventional synchronous-generator-based power systems
(fuel dominant) to future converter-based highly-integrated energy systems
(renewable dominant).
2
Conventional fossil-fuel-based power plants have large synchronous
generators, capable of supporting the grid by several important ancillary services,
such as providing a large amount of fault current which is of great importance to
support grid voltage and activate protective relays. In contrast, emerging converter-
interfaced power units, such as different types of renewable-based distributed
generation (DG) units as well as grid-interactive microgrids and HVDC systems,
have several challenges in supporting the grid stability. For example, converter-
interfaced DG units can typically provide only 1–2 pu fault current depending on
their semiconductor capabilities [6]. In addition, the control systems of converter-
based units are sensitive to grid voltage deviations and thus increasing requirements
have been imposed by transmission system operators for low-voltage ride-through
(LVRT) and voltage support capabilities [7], [16], [41]-[42]. Numerous projects are
consequently conducted worldwide to tackle the corresponding reliability and
stability challenges in the coming power system era. “MIGRATE” project under
the European Union framework [8], “Synchronous Condensers Application in Low
Inertia Systems” in Denmark [9], and the “ProSmart” project in Norway [10] are
just few examples of the extensive effort to address the grid reliability and stability
concerns in future highly-integrated and low-inertia power systems.
During unbalanced conditions, the operation of converter-interfaced units is
prone to even more undesirable functions, such as distortions on the output current
and oscillations on the dc-link voltage and output power. These adverse situations
can severely harm the operation of a power system and, if not managed properly,
cause a cascading failure. A variety of control techniques, which are mainly based
on the symmetric sequences, have thus been proposed to ride through grid faults by
converter-interfaced units [11]-[16]. However, there are still different challenges
remained which need further research and development such as improved operation
of individual units and smart coordination between multiple units under the grid
faults.
Grid-interactive smart inverters (GSIs) are becoming very popular both in
research [66]-[68] and industry [69]-[70] which encorpoate smart functionalities
inside the grid-tied converters. These grid-tied converters are widely used for
3
integrating modern power units such as different types of renewable energies,
energy storage systems, electric vehicles, solar roofs, DG units, hybrid microgrids,
and HVDC systems [17]-[21]. Smart inverter functionalities refer to fast and
reliable response of GSIs to grid abnormalities such as LVRT, voltage support,
frequency ride-through, volt/var or volt/watt control, off-unity power factor,
dynamic reactive current injection, etc. [66]-[70]. These functionalities can be
achieved by central networked supervisory systems or advanced embedded control
techniques. Expected high integration of smart inverters inside future energy
systems brings unprecedented opportunities for optimized operation of energy
systems and booming growth for clean technologies. Therefore, this research
project focuses on proposing advanced control techniques for optimal operation of
GSI units under asymmetric grid conditions.
1.2 State-of-the-Art For a decade, the proper operation of converter-based units under the grid faults,
also known as the LVRT capabilities, is one of the hottest area in the literature
among the power system studies. Numerous efforts have thus been carried out for
improving the LVRT capabilities in converter-interfaced DG units [22]-[59],
doubly-fed induction generators [60]-[62], and HVDC transmission systems [63]-
[64]. The studies of the LVRT capabilities in the converter-interfaced DG units
have mainly focused on the following five areas:
quality of the injected current [11]-[16],
reduction of oscillations on dc-link voltage and output active power [22]-
[25],
flexible oscillations on the output active and reactive powers [26]-[27],
point of common coupling (PCC) voltage support schemes [26]-[53], and
maximum allowable support to the grid [42], [51], [54].
Here, the recent accomplishments in each category are briefly discussed in
order to give a glimpse into the state-of-the-art. The most recent work on the quality
of the injected current under unbalanced grid faults [11] presents a model-based
4
control design to improve the dynamic performance of the grid-connected
converters and enhance the fault current transients.
Reference [13] proposes a series of control strategies and corresponding
circuit configurations which utilize the zero sequence components to enhance the
power controllability and eliminate active power oscillations. For the flexible
control of oscillations on the output active and reactive powers, different strategies
based on symmetric-sequence components are proposed in [27], yielding an
adaptive controllability that can manage multiple objectives and constraints. It is
shown that active and reactive power oscillations can be independently regulated
with two individually adaptable parameters. In a range of variation for these
parameters, the amplitudes of oscillating power can be also slightly controlled, as
well as the peak values of the output currents. For instance, the oscillating active
power can be limited below a certain amount while the output currents are
controlled to be as balanced as possible.
In the available literature, the voltage support schemes, by converter-
interfaced DG units under unbalanced grid conditions, can be themselves
categorized based on the following notions:
voltage support based on the grid code requirements [36]-[40]
voltage support based on the maximum allowable reactive power delivery
[41]-[42]
flexible voltage support based on the positive and negative sequence
compensation [27], [43]-[45]
phase voltage regulation by positive and negative sequence compensation
[46]-[51]
phase voltage regulation by positive, negative and zero-sequence
compensation [52]-[53].
In [36]-[40], for supporting the PCC voltage under unbalanced grid faults, the
idea is to follow the imposed rule by German E.ON grid code [65], requiring the
reactive current injection proportional to the balanced voltage depth. This is a
primitive solution because it over-simplifies the problem and does not consider
5
unbalanced fault characteristics and other parameters, such as grid impedance and
over-voltage issues in unfaulty phases. In [42], it is proposed to utilize the entire
available capacity of the converter to inject the reactive current for supporting the
PCC voltage. This strategy also suffers from similar problems. However, the idea
of the German grid code for balanced faults has been extended in [44] to consider
unbalanced faults by proposing simultaneous positive and negative reactive current
injection, respectively, proportional to the depth of the positive voltage component
and raise of the negative voltage sequence. Although the strategies in this category
(i.e., flexible positive and negative voltage support strategies [43]-[45]) aims to
consider unbalance factor, they still lack taking into account grid impedance and
over-voltages on unfaulty phases. To address these problems, the methods proposed
in [46]-[51] shift the view toward regulating the phase voltages within the pre-set
boundaries by positive and negative sequence control. These methods are revised
in [52]-[53] to improve their accuracy by considering the zero-sequence
compensation. Reference [53] presents the positive-, negative-, and zero-sequence
voltage and current control schemes, with dynamically varying limits, in dq-frame
for the converter-based DG units in order to compensate voltage unbalance in a
microgrid.
References [42] and [55] overview the conventional reference current generation
strategies and propose analytical approaches to provide their maximum allowable
support capabilities considering the limitation on the peak value of the three-phase
currents.
1.3 Motivations and Objectives
Motivated by the aforementioned concerns, this research project focuses on
proposing new solutions for improved performance of grid-connected smart
inverters under unbalanced grid conditions and asymmetric short-term faults. In this
regard, the followings are the main objectives of this research project.
First stage:
6
• comparative studies of the available control strategies under
unbalanced conditions for evaluating their supporting capability,
• proposing maximum asymmetric support scheme based on the
analytical studies,
• proposing a novel reference current generation scheme aiming to
minimize the power oscillations and maximize the average active or
reactive power delivery, considering the phase current limits,
• proposing a control technique to minimize the fault current with the
existing set-points for the output active and reactive powers.
Second stage:
• proposing the comprehensive asymmetric ride-through (ART)
regulation scheme,
• enforcing large DGs to properly regulate the phase voltages within the
pre-set dynamic limits under short-term asymmetric low voltages,
• proposing an advanced dynamic voltage regulation method to
accurately address the ART specifications.
Third stage:
• proposing a novel voltage support scheme with improved accuracy in
regulating the phase voltages at the PCC within the pre-set safety limits,
by considering the zero-sequence voltage component,
• considering the output active power in the improved asymmetrical
voltage support and being adaptive to complex grid impedance (i.e.
with resistive and inductive parts),
• augmenting the limited active power oscillation strategy to the
proposed voltage support scheme, which provides an adjustable dc-link
voltage oscillation setting while simultaneously supporting the host ac
grid, even under severe unbalanced faults,
7
• augmenting the maximum active power delivery strategy to the
proposed voltage support scheme to enable it with the maximum
asymmetric support (MAS) capability.
Fourth stage:
• coordinating the maximum flexible asymmetrical voltage support and
ride-through capability of parallel-operated multi inverter structure,
• maximizing the collective dynamic contribution of parallel-operated
multi inverter structure in boosting the voltage and reducing the
imbalance subject to the constraints of the plant and host system,
• keeping the active power injection of each unit intact during the support
which leads to power/cost saving in the plant operation as well as host
system stability enhancement.
Fifth stage:
• decentralized maximum flexible asymmetrical voltage support tracking
in distributed multi inverter structure that does not need communication
and central control unit,
• keeping the active power injection of each distributed unit intact during
the support,
• introducing new concepts such allowable flexible support areas and
support points trajectories represented in the negative-reactive-current
vs. positive-reactive-current plane.
1.4 Thesis Outline
The thesis is organized as follows (the contributions of each chapter are briefly
presented here):
8
Chapter 2: Maximum Asymmetric Support (MAS) in A Grid-Interactive
Smart Inverter
This chapter presents a novel reference current generation scheme with the
ability to support the grid voltage by injecting optimal sets of positive/negative
active/reactive currents. Analytical expressions are proposed in order to find the
optimal values of the controlling parameters under any unbalanced grid voltage
condition. The optimal performances can be obtained by achieving the following
objectives: (1) compliance with the phase voltage limits, (2) maximized active and
reactive power delivery, (3) minimized fault currents, and (4) reduced oscillations
on the active and reactive powers. These optimal behaviors bring significant
advantages to emerging GSIs, such as increasing the efficiency, lowering DC-link
ripples, improving AC system stability, and avoiding equipment tripping.
Chapter 3: Asymmetric Ride-Through (ART) Guidelines
This chapter highlights the necessity of supporting the connection voltage by
large DG units under short-term unbalanced voltage sags. To address this, a new
regulation scheme, named ART scheme, is proposed. The proposed scheme
enforces DG units to properly regulate the voltage within the dynamic limits for
three important voltage parameters: positive-sequence, negative-sequence, and
phase voltage magnitude. The main advantages of applying the ART scheme are
avoiding unnecessary outages due to temporary unbalanced faults and enhancing
the grid stability. As the second contribution, a dynamic voltage regulation method
is also proposed to accurately address the specifications determined in the ART
scheme.
Chapter 4: Advanced Asymmetric Voltage Regulation and MAS Scheme in
A Single Grid-Interactive Smart Inverter
This chapter proposes an advanced voltage support scheme in a GSI, to
accurately regulate the three-phase voltages of the connection point. The proposed
scheme not only compensates the zero-sequence component but also considers the
active power injection. Unlike the conventional methods, the proposed support
method is adapted even in resistive distribution systems. Moreover, the adjustable
9
limited active power oscillation strategy is added to the proposed method. This
feature limits the oscillation to a specified value which provides an adjustable DC-
voltage oscillation setting while simultaneously supporting the AC host grid, even
under severe unbalanced faults. Third, the MAS equations are formulated for the
new method.
Chapter 5: Parallel MAS Scheme in Multiple Parallel-Operated Grid-
Interactive Smart Inverters
The analyses in this chapter show that the MAS techniques presented in the
previous chapters are not sufficient to provide the overall optimal asymmetric
support of the parallel-operated multi-inverter system. This paper thus proposes a
new methodology to: (1) coordinate the asymmetrical ride-through and voltage
support capabilities of different parallel-operated GSI units, (2) maximize the
utilization of each unit and their overall collective contribution in boosting the
positive-sequence voltage and reduction of the negative-sequence voltage subject
to the constraints from both DG and grid points of views. The simulation tests on a
parallel multi-inverter structure, i.e., the ABB 2.0 MVA central inverters, illustrate
the promising results of the proposed algorithms.
Chapter 6: Decentralized MAS Scheme in Multiple Distributed Grid-
Interactive Smart Inverters
This chapter proposes a comprehensive autonomous coordination control
scheme to achieve cooperative asymmetric low-voltage ride-through and grid
support by multiple distributed GSI units in an active distribution network. In
addition to the decentralized nature of the proposed coordination scheme, it
provides three important features: 1) a maximized flexible asymmetrical voltage
support that does not affect the active power injection of individual units at the time
of the support, 2) maximum support point tracking of each unit considering current,
voltage, and power constraints, and 3) wise dynamic support points movement. The
proposed scheme is examined in a practical test system, adapted from Hydro One
27 kV medium-voltage active distribution network in Ontario, Canada. Test results
10
demonstrate significant improvements obtained from the proposed methodologies
compared to the conventional techniques.
1.5 Summary of the Key Contributions
The contributions of this thesis to the research field can be summarized as follows:
1) The MAS scheme is proposed by advanced control techniques with multi-
objective optimization in a single inverter structure. The proposed MAS
scheme has three fundamental criteria:
a. The asymmetric voltage is flexibly supported in positive and
negative sequences.
b. The flexible voltage support has minimal impact on the output
power (e.g., average value and oscillation amount).
c. The peak current limitation of the power electronic switches is
respected.
2) The ART regulation guidelines are proposed enforcing large DGs to
properly regulate the phase voltages within the pre-set dynamic limits
under short-term asymmetric low voltages. Further, an advanced dynamic
voltage regulation method is also suggested to accurately address the
ART specifications.
3) Unique MAS techniques are proposed for multiple GSI units in the
parallel structure which enables the maximum collaboration between the
units in flexible and optimized asymmetric voltage support. This method
is called parallel MAS (PMAS) technique.
4) Another unique MAS scheme is proposed for the autonomous
coordination control of multiple GSI units in the distributed structure.
This scheme is named decentralized MAS (DMAS). While achieving a
superior coordination between the MAS performance of each GSI, the
DMAS eliminates the dependency of the control system to
communication infrastructure.
11
Chapter 2
Maximum Asymmetric Support (MAS) in
A Grid-Interactive Smart Inverter
2.1 Introduction
Recently, riding through grid faults and supporting the grid under abnormal
conditions by grid-interactive smart inverters (GSIs) have become increasingly
attractive. This chapter presents a set of optimized reference current generation
strategies with the ability to support the grid voltage by injecting a proper
combination of positive/negative and active/reactive current components.
As the main contribution, this chapter utilizes a new control scheme with
analytical expressions capable of finding the optimal values for four control
parameters under any unbalanced grid voltage condition to achieve the following
objectives:
• minimized oscillations on the active and reactive powers,
• boosted and semi-balanced phase voltages of the PCC,
• minimized inverter fault current, and
• maximized active and reactive power delivery.
To fully accomplish these objectives, the expressions of the boosted phase
voltages, maximum oscillations on instantaneous active/reactive powers, and the
12
maximum phase currents under the unbalanced conditions must be found.
Maximum allowable support scheme is also proposed to obtain the maximum
allowable active or reactive powers which the inverter can deliver to the grid under
unbalanced conditions (to support either the grid voltage or the grid frequency)
without exceeding the phase current limit, Ilimit. The mathematical equations of the
control schemes under various conditions (i.e., various voltage dip characteristics,
several system parameters, different operating points, etc.) are obtained and
presented in the coming sections. Different simulation and experimental test cases
are used to verify the accuracy and effectiveness of the proposed control schemes.
2.2 System Description
In this chapter, the flexible reference current generation strategy is initially
presented for the GSI system, shown in Fig 2.1. Then, it will be utilized to build
different control techniques. This flexible reference current generation strategy can
flexibly contain positive/negative and active/reactive current components, offering
valuable voltage support services with two controlling parameters, kp and kq, as well
as set points for the average active and reactive powers, P* and Q*. The total
reference current can be formulated by using four components as
* *
2 2
* *
2 2
, (1 )( ) ( )
, (1 )( ) ( )
p p q q
p p p p p p
q q q q q q
i i i i i
P Pi k v K v i k v K vV VQ Qi k v K v i k v K v
V V
+ − + −
+ + + + − − − −+ −
+ + + + − − − −⊥ ⊥ ⊥ ⊥+ −
= + + +
= = = − =
= = = − =
(2.1).
Also, the voltage under single-phase unbalanced condition can be simplified as [42]
cos ( t) cos ( t),
sin ( t) sin ( t)
sin ( t) sin ( t),
cos ( t) cos ( t)
v vV Vv v
v vV V
v vV Vv v
v vV V
α α
β β
α α
β β
ω ω
ω ω
ω ω
ω ω
+ −+ −+ −
+ −+ −
+ −+ −⊥ ⊥+ −
⊥ ⊥+ −+ −⊥ ⊥
− = = = = − − = = = = −
(2.2).
13
R LRg Lg
Zfault
Rf Lf
Cf
S1 S2 S3
S4 S5 S6Cdc
DC Chopper
Rchopper
PDG
v vg
i
DG UnitGridPCC
vmeasimeasVdc,meas PWM Control mabc Load
GCC
Circuit topology of the grid-interactive inverter.
In this section, the equations of oscillatory terms on active and reactive
powers ( maxp and maxq ) are obtained from reference current of Eq (2.1). The detailed
derivation of the instantaneous active/reactive power is provided in Eq (2.3).
2
. ( ).( ) . . . .
(1 ) / cos (2 ) (1 ) / sin (2 )
. ( ).( ) . . . .p p q q
s
pP
p v i v v i i v i v i v i v i
P P k n P k n t Q k n Q k n t
q v i v v i i v i v i v i v i Q q
ω ω
⊥ ⊥ ⊥ ⊥ ⊥ ⊥
+ − + − + + − − + − − +
+ − + − + + − − + − − +⊥
= = + + = + + +
= − × − + × × − × − − × × = = + + = + + + = +
2
(1 ) / sin (2 ) (1 ) / cos (2 )
c
p p q q
q
Q P k n P k n t Q k n Q k n tω ω
+
= + × − − × × − × − + × ×
(2.3).
where n is the ratio between the negative-sequence and positive-sequence voltages.
The ability to analytically calculate the maximum power oscillations, i.e. maxp and
maxq , in terms of the scalar parameters (i.e., P, Q, kp, kq, and n) is very useful for
proper controlling of the GSIs under generic voltage condition. Therefore, the
expressions of maxp and maxq is obtained as
2 22 1 2 1max (1 ) (1 )p p q qp P k n k n Q k n k n− − = + − + − −
2 22 1 2 1max (1 ) (1 )q q p pq Q k n k n P k n k n− − = + − + − − (2.4).
In this chapter, these equations are used to minimize the oscillations on active
and reactive powers. By applying Eq (2.2) in (2.1), the injected current under the
fault can be rewritten in the αβ frame:
14
, , , ,
, , , ,
...
cos ( ) sin ( )
sin ( ) cos ( )
p p q q
p p q q
p p q q
p p q q
i i i iii i i i i
K V K V t K V K V t
K V K V t K V K V t
α α α αα
β β β β β
ω ω
ω ω
+ − + −
+ − + −
+ + − − + + − −
+ + − − + + − −
= + + + = − − + = + + −
(2.5).
The αβ currents of Eq (2.5) are transformed into the abc currents by the
transformation matrix. Therefore, the maximum currents in each phase can be
obtained as
2 221 2max a
2 2 23 31 1max b 1 4 2 32 2 2 22 2 23 31 1max c 1 4 2 32 2 2 2
( ) ( )
( ) ( )
( ) ( )
K KI
I K K K K
I K K K K
−
−
−
+ = − + + + − − + −
, where
( )( )
( )( )
1
2
1 1
1 1
p p p
q q q
PK K V K V n kVQK K V K V n kV
+ + − −−
+ + − −−
= − = + −
= + = − +
( )( )
( )( )
3
4
1 1
1 1
p p p
q q q
PK K V K V n kVQK K V K V n kV
+ + − −−
+ + − −−
= + = − + = − = + −
(2.6).
2.3 Proposed Multi-Objectively Optimized Control
Strategies
In this section, five strategies are initially proposed:
1) minimized active power oscillation,
2) minimized reactive power oscillation,
3) minimized fault current,
4) maximum allowable active power injection, and
5) maximum allowable reactive power injection.
15
It is suggested that some of these objectives can be combined to
simultaneously benefit their advantages. In the next section, an advanced strategy
will be also proposed which not only provides the maximum allowable active power
injection but also aims to regulate the phase voltages within the desired limits.
2.3.1 Minimum Oscillation on the Active and Reactive Powers
By taking the derivative of Eq (2.3) in terms of kp and kq, and finding the extreme
point by enforcing the derivatives to be zero, the following expression can be easily
obtained for the minimum oscillations on the instantaneous active and reactive
powers:
( )( )
2
max 2
1/ 1minimum when
1/ 1
p
q
k np is
k n
= −
= + ,
( )( )
2
max 2
1/ 1minimum when
1/ 1
p
q
k nq is
k n
= +
= − (2.7).
These strategies are called minimum oscillation on the active (or MOP) and
reactive (or MOQ) powers. For an efficient power delivery, the kp and kq values are
set to be only between 0 and 1 [13], [49]. Since Eq (2.7) gives a kp (or kq) value
greater than 1, it can be changed to kp=1. In this case, only positive sequence active
currents will be injected while the reactive currents will contain both positive and
negative components based on 1/(1+n2). However, kp (or kq) can be set to be 1/(1-
n2) in certain applications when minimizing the active (or reactive) power
oscillations is critical. To improve the MOP strategy, P* or Q* can be obtained by
using the proposed MAP or MAQ expressions, presented in next sections,
respectively. Therefore, the objectives of both strategies, e.g., MOP and MAQ, can
be simultaneously accomplished. Similarly, MOQ can be also combined with MAP
strategies in order to achieve double objectives.
16
2.3.2 Minimum Fault Current (MFC) Strategy
To obtain the minimum fault currents, Eq (2.6) should be considered. According to
Eq (2.6), the maximum phase current can be one of the three expressions. For the
proposed MFC scheme, the reference values for the active and reactive powers can
be determined from the operating mode controllers (either PV or PQ modes) or
from the grid code requirements. Also, the value of kq can be obtained from the
voltage support scheme introduced in the next section. Therefore, the minimum
point of each expression of Eq (2.6) should be obtained by taking their derivatives
with respect to kp:
min ,a min ,b 2
min ,c 2
(2 ) 3 (2 1)1 ,1 2 ( n 1)
(2 ) 3 (2 1)
2 ( n 1)
qa p b p
qc p
P n nQ kI k I k
n P n
P n nQ kI k
P n
− −
−
× − + × −⇒ = ⇒ =
+ × − +
× − − × −⇒ =
× − +
(2.8).
However, only Eq (2.8) cannot fully ensure that the obtained kp will always
minimize Imax in Eq (2.6) because these equations minimize only their
corresponding currents, i.e., Imax-a, Imax-b, and Imax-c. Therefore, it is suggested in this
chapter that, in addition to the three kps obtained in Eq (2.8), three other kps should
be also considered to find the optimum value, kp,opt. Two of these kps are the
intersections of the magnitude curve of Ia(kp) with the magnitude curves of Ib(kp)
and Ic(kp). Therefore, the equations of Ia and Ib, as well as Ia and Ic are taken to be
equal in order to find kp,ab and kp,ac, respectively.
22
2,ab
2
22
2,ac
2
34( ) ( ) 3 3 (2 1)
23 (1 ) 3
34( ) ( ) 3 3 (2 1)
23 (1 ) 3
a p b p p q
q q q
a p c p p q
q q q
a nPb b acI k I k k b nP nPQ k
ac nk Q k nPQk
a nPb b acI k I k k b nP nPQ k
ac nk Q k nPQk
=− + − = ⇒ = = − + −
= − − =− + − = ⇒ = = − − −
= − +
(2.9).
Since kp is bounded to 1, kp,1=1 should be also considered in order to find the
minimum phase currents and optimal kp value, i.e. Imax,opt and kp,opt. Therefore, the
17
three phase currents are calculated for six possible kps in order to find the minimum
Imax. This chapter suggests that the kp,opt, can be calculated under any operating and
fault condition for any P, Q, V+, and V- values.
2.3.3 Maximum Allowable Active and Reactive Powers Strategies
Applying the maximum allowable active power (MAP) strategy provides the
maximum active power to the grid for assisting the frequency stability while
simultaneously respects the phase current limits. The required equations of PMAP
should be obtained such that they guarantee none of the phase currents under the
abnormal condition passes the pre-set limits, Imax. In this strategy, the reference
value for Q is determined either by the V-Q droop control or grid code
requirements. By using the Imax equations of Eq (2.6), three possible active power
values can be obtained as
( )( )
2 2max 2
12
2
3 2
1
4 / 2
4 / 2
p p
V I Kk n kP
P b b ac a
Pb b ac a
− − + −
= − + − + −
, where
2 2
4 2
2 2 22 4 max
3 1( ( 1) 1) ( ( 1) 1)
2 3 ( ( 1) 1) ( ( 1) 1)
3 4
p p
p p
a k n k nV V
K Kb k n k nV V
c K K I
− −
− −
= − + + + − = + − − − + = + −
(2.10).
In order to have all of the three-phase currents of Eq (2.6) lower than the pre-set
Imax value, 𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀∗ should comply with *1 2 3min( , , )MAPP P P P= .
Similarly, the maximum allowable reactive power (i.e. MAQ strategy) aims
to provide reference value of 𝑄𝑄𝑀𝑀𝑀𝑀𝑀𝑀∗ such that all phase currents remain bounded
with the current limit. The reference value of P is determined by other controllers
18
in the GSI (e.g., by maximum power point tracking), and the 𝑄𝑄𝑀𝑀𝑀𝑀𝑀𝑀∗ expressions can
be obtained by using the Imax equations of Eq (2.6):
( )( )
2 2max 1
12
2
3 2
1
4 / 2
4 / 2
q q
V I Kk n kQ
Q b b ac a
Qb b ac a
− − − +
= − + − + −
, where
2 2
3 1
2 2 21 3 max
3 1( ( 1) 1) ( ( 1) 1)
2 3 ( ( 1) 1) ( ( 1) 1)
3 4
q q
q q
a k n k nV V
K Kb k n k nV V
c K K I
− −
− −
= + − + − + = − + − + − = + −
(2.11).
To satisfy min (Ia,Ib,Ic) ≤ Imax, 𝑄𝑄𝑀𝑀𝑀𝑀𝑀𝑀∗ can be obtained as *1 2 3min( , , )MAQQ Q Q Q= .
2.4 Voltage Support Strategy
Supporting the PCC voltage by using DG units is another objective proposed in this
chapter. If the DG plant rated power and the grid impedance are not small, then,
under the moderate sags, the three-phase voltages can be regulated at the desired
range between Vmin and Vmax. In [49], the proposed scheme has been applied only
in the STATCOM application, where the reference current contains only the
reactive components. The principal objective in the voltage support is to avoid the
over-voltage and under-voltage at the PCC whenever possible. However, a proper
solution can be found in this range in order to satisfy other objectives as well.
Unlike [49], this chapter considers the active components of the current. The PCC
voltage support strategy (VSS) can be extracted as a function of the grid voltage
and the injected positive and negative currents:
19
( ) ( )( ) ( )
g g g g
g g g g
d i iv v L R i iv v dtv v v
v v d i iv v L R i i
dt
α αα α α αα α
β β β ββ β β β
+ −+ − + −+ −
+ −+ − + −
+ − + −
+ + + + + + = + = = + +
+ + + +
(2.12).
Applying Eq (2.6) and (2.2) in (2.12) gives the following:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )( )( ) ( )( )
( ) ( )( )( ) ( )( )
1 2 1 2
3 4 3 4
cos cos
sin sin
sin cos cos sin
sin cos cos sin
g g
g g
g g
g g
V V t V V t
V V t V V t
L K t K t R K t K t
L K t K t R K t K t
ω ω δ
ω ω δ
ω ω ω ω ω
ω ω ω ω ω
+ − + −
+ − + −
− − − = + + −
− + + + + − + +
(2.13).
In practical applications, δ is small and can be neglected for the simplicity in
the analytical solution. Then, the positive and negative components of (2.13) can
be separated as
g g q g p
g g q g p
V L I R IV
V V L I R I
ω
ω
+ + ++
− − − −
− = + −
(2.14).
The maximum and minimum phase voltages can be determined simply by
( ) ( ) ( )( )
( ) ( ) ( )( )
2 2
abc min min
2 2
abc max max
min( , , ) 2
max( , , ) 2
a b c
a b c
V V V V V V V V
V V V V V V V V
λ
λ
+ − + −−
+ − + −−
= = + +
= = + +, where
( ) ( ) ( )( )( ) ( ) ( )( )
2 2min 3 3
2 2max 3 3
min cos ,cos ,cos ,
max cos ,cos ,cos
π π
π π
λ γ γ γ
λ γ γ γ
= − +
= − + (2.15).
Then the reference values for the maximum and minimum phase voltages can
be determined so that the phase voltages are regulated within the explained
thresholds. The reference values for V+ and V- can be calculated as
20
( ) ( )( )
( ) ( )( )
2 22 2 2 2 2 2max min min max max min min max min max
max min
2 22 2 2 2 2 2max min min max max min min max min max
max min
2ref
ref
V V V V V VV
V V V V V VV
λ λ λ λ
λ λ
λ λ λ λ
λ λ
+
−
− + − − −=
−
− − − − −=
−
(2.16).
By using Eq (2.16), the reference values for the desired positive and negative
sequences of the voltage are obtained. Then, V+ and V- in (2.14) are replaced with
the reference values obtained from (2.16). Moreover, positive and negative
sequences of the grid voltage can be estimated from the PCC measurements.
Therefore, (2.14) can be rewritten as
2 2 2 2
2 2 2 2
, ,
,
p ref p ref
q ref q ref
R RI V I VX R X R
X XI V I VX R X R
+ + − −
+ + − −
= ×∆ = ×∆+ +
−= ×∆ = ×∆
+ +
(2.17).
For an inductive grid, (2.17) can be simplified as
0, ,ref refp p q q
V VI I I I
X X
+ −+ − + −∆ −∆= = = = (2.18).
2.5 Maximum Asymmetric Support (MAS) Scheme
This thesis proposes a new supportive scheme under unbalanced grid conditions
which combines the control strategies introduced in the previous sections. This
scheme is named maximum asymmetric support (MAS) and denotes a set of
strategies that empowers GSIs to flexibly support the asymmetric voltage up to their
maximum capability, e.g., supporting both positive- and negative-sequence
voltages by a GSI while retaining its maximum power delivery capability with
respect to its peak-current limitation.
A simple example of the MAS scheme can be the combination of the
proposed VSS and MAP strategies in the previous sections. Hence, the objectives
of both strategies are simultaneously accomplished:
21
1) regulating the phase voltages within the pre-specified boundaries,
2) injecting the maximum active power, and
3) respecting the pre-defined current limit, Imax.
If the X/R ratio of the system is high, the active current components of Eq
(2.17), i.e., pI + and pI − , do not contribute significantly in regulating the voltage.
Consequently, the voltage support should be completely accomplished by the
reactive currents, and the active current components can be used to inject the
maximum allowable active power with respect to the current limitation.
2.6 Simulation Results
Fig 2.1 illustrates the circuit topology of a GSI-interfaced DG unit (210 kVA, 690
V, and 60 Hz). A dc power supply can be used to emulate the renewable energy
resources and storage in the dc-link [13], [49]. A type B fault (phase A to ground)
occurs with a significant voltage dip on phase A as indicated in Fig 2.2(a). System
parameters are reported in Table 2.1.
TABLE 2.1 Simulation Test System Parameters
Zg (mΩ) 7+ j2πf×90e-3 VDC (V) 1200
Z (mΩ) 1 VL-L, RMS (V) 690
Zf (mΩ) 0.8 f (Hz) 60
Irate (A) 200 S (kVA) 210
Kp-cc 0.05 Ki-cc 1
Kp-pll 180 Ki-pll 3200
22
2.6.2 Test Case A: Performance Evaluation of MOP and MOQ
Strategies
In normal operation, kp and kq both are set to be 1, and consequently, pure positive
sequence current injection is applied. Between t1=0.3s and t2=0.6s, a moderate
voltage dip happens where Va = 0.5 pu., and a solid one-phase fault is emulated
after t2=0.6s. Here, P and Q are set to be 100 kW and 30 kVAR. kp and kq are
obtained according to Eq (2.7). According to 0, the oscillations on the active and
reactive powers are eliminated after applying the MOP and MOQ strategies,
respectively.
(a) (b)
Simulation results of MOP and MOQ Strategies: (a) PCC voltage, and (b) active/reactive powers.
2.6.3 Test Case B: Performance Evaluation of VSS-MAP Strategy
This test case shows the performance of the proposed VSS-MAP strategy. Four
different voltage sags occur for one phase of the grid voltage in t=0.1, 0.25, 0.4,
0.55 s, respectively. To clearly illustrate the performance of the proposed VSS
method, a 0.05 delay is considered after all the fault occurrences in order to compare
the results before and after applying the VSS strategy. Fig 2.3 shows that by
applying this strategy, all three phases are regulated in the desired range of Vmin=0.9
pu and Vmax=1.1 pu. In t=0.4 s, the voltage sag in phase A is 0.25pu (0.15 pu below
Vmin), so boosting Va with 0.15 pu by using only the positive reactive current will
cause overvoltage in the other two phases. In order to tackle overvoltage in the other
23
two phases, the proposed VSS strategy is applied to inject the required negative
reactive current as well as the positive reactive current (see Fig 2.3(b)). In addition
to showing the applied VSS strategy, Fig 2.3 demonstrates that the MAP strategy
has also determined the maximum active power where the three phase currents are
under the pre-set limitation, i.e., Imax=200 A. Therefore, the objectives of both
strategies are simultaneously accomplished in this test case: (i) the phase voltages
have been regulated within the pre-specified boundaries, (ii) the maximum active
power has been injected to support the grid, and (iii) all three-phase currents are
limited to the pre-specified current limitation, Imax.
(a)
(b)
(c)
(d)
Simulation results of VSS-MAP Strategy: (a) magnitude of phase voltages, (b) positive/negative and active/reactive components of currents, (c) phase currents, and (d)
active/reactive powers.
2.7 Experimental Results
To verify the analytical expressions, the experimental test system, shown in Fig 2.4,
is also employed. This system contains a voltage source converter connected to the
24
grid and operated in the PQ mode. A Semistack intelligent power module consisting
of gate drives and six insulated gate bipolar transistors (IGBTs) is used to
implement the GSI. The switching frequency is 10 kHz. The converter is interfaced
to a dSPACE1104 control card via a CMOS/TTL interfacing circuit. The converter
is connected to a 60-Hz, 110-V (phase-voltage) three-phase grid via a three-phase
transformer. Other parameters are reported in [51]. The proposed schemes are
implemented on the dSPACE for switching-signal generation.
Experimental test setup.
2.7.2 Experimental Test Case A: MFC Strategy
This test case shows the results of the MFC strategy. In this case, P=100 W and
Q=175 VAr are injected by the GSI. Again, a similar phase-to-ground fault occurs
at t=2.6 s. In this test case, kq is taken to be 0.8 after the fault occurrence. After it,
the phase currents increase up to 9.5 A. At t=11 s, the MFC strategy is activated.
The activation changes the value of the kp from 1 to 0.79 in order to minimize the
maximum phase current. Using the MFC strategy, the optimum kp value is obtained
by having three known parameters (i.e., P=100 W, Q=175 VAr, and kq=0.8) and
the fault characteristics. The MFC strategy reduces the phase currents to 8 A, as Fig
2.5(b) illustrates.
25
2.7.3 Experimental Test Case B: MAQ Strategy
This test examines the effectiveness of the proposed MAQ. Here, P=150W is
injected. A similar phase-to-ground fault occurs in t=1.5 s. Under the fault, the
voltage profile drops from 30V to 25V (%16.6 voltage drop). At t=4.3 s, the MAQ
scheme is triggered with the predefined Ilimit=10A, as shown in Fig 5. In practical
applications, this scheme can be triggered automatically and immediately after the
fault. However, it is configured manually in this test to show the results before and
after applying the MAQ. According to Fig 2.6 (a), the PCC voltage is increased to
29V after applying the MAQ. Also, the injected currents are limited to 10A, as
indicated in Fig 2.6(b).
(a)
(b)
Experimental results of the MFC strategy: (a) faulted voltage, (b) currents.
26
(a)
(b)
(c)
Experimental results of MAQ: (a) faulted voltage, (b) phase currents, (c) active and reactive powers.
(a)
(b)
(c)
Experimental results of MAP: (a) faulted voltage, (b) phase currents, (c) active and reactive powers.
27
2.7.4 Experimental Test Case B: MAP Strategy
This test case provides the grid code requirement for the Q injection during the low-
voltage and investigates the application of the MAP strategy. In this test case,
P=225W is initially injected by the GSI, as indicated in Fig 2.7(c). Similarly, a
phase-to-ground fault occurs in t=2. This fault causes the PCC voltage to drop from
30V to 25V. At t=4.3s, the reactive power imposed by the grid code requirement is
injected. This injection causes the PCC voltage to increase to 26V, as shown in Fig
2.7(a). At t=8.6s, the MAP strategy is activated to inject the maximum allowable
active power with respect to Ilimit=10A. As shown in Fig 2.7(b), the abc currents are
limited to 10A under the unbalanced fault and after applying MAP scheme.
2.8 Conclusion
This chapter presented multi-objectively optimized reference current generation
schemes by injecting a proper set of positive/negative active/reactive currents using
four controlling parameters. Analytical expressions were proposed in order to find
the optimal values of these parameters under generic grid voltage condition. The
proposed schemes aim to regulate the three phase voltages, minimize power
oscillations, minimize fault currents, and maximize power delivery, under low
voltage and unbalanced conditions. Depending on the available controlling
parameters, two or three of these objectives can be achieved simultaneously, but
not all of them since there are only four controlling parameters. This multi-objective
optimized operation has substantial advantages in the increasing integration of
GSIs, such as improving the efficiency, lowering DC-link ripples, increasing AC
system stability, complying with stringent grid codes, and avoiding equipment
tripping. The successful results of the proposed schemes were verified using
simulation and experimental test results.
28
Chapter 3
Asymmetric Ride-Through (ART)
Guidelines
3.1 Introduction
The integration of renewable energy resources and DG units is
remarkably increasing with no signs of slowing down. For more than a decade,
system operators have been updating their grid codes to address the reliability
concerns of such integrated grids [71]-[74]. First, this chapter briefly overviews the
LVRT requirements and trends in different countries [72]-[83]. Then, a new
scheme, called asymmetric ride-through (ART), is proposed in this chapter to
enhance the system reliability under the short-term unbalanced faults. The ART
scheme aims to enforce large DG units not only ride-through the asymmetrical grid
faults, but also support the grid by proper measures. Based on the proposed scheme,
DG units are required to withstand the short-term unbalanced low-voltages under
certain circumstances. In the ART scheme, specific dynamic boundaries are
developed for three voltage parameters (i.e., positive-sequence, negative-sequence,
and magnitudes of phase voltages). If a DG with a proper voltage support strategy
can meet the proposed requirements for these three voltage parameters, it will
have a successful ART performance. The proposed regulation scheme can be very
29
beneficial for the growing integration of DG units as well as other converter-
interfaced units such as grid-interactive micro-grids, and HVDC systems.
In section 3.4, this chapter also overviews the voltage support strategies
(VSSs), under unbalanced conditions, presented in the recent works [36]-[53].
These strategies are categorized into four groups and briefly discussed. The
compliance of the reviewed four VSS groups [36]-[53] with the proposed
ART scheme is studied in section 3.5. Then, a new ART-adaptive voltage support
(ART-VS) method is proposed to enable DG units to meet the ART requirements.
The proposed ART-VS method has the following advantages:
1) supporting the phase voltages under any unbalanced faults to the
maximum capability of the DG,
2) preventing phase voltages from exceeding the boundaries proposed in the
ART scheme by proper combination of voltage boost and unbalance
reduction,
3) being adaptive to the dynamic ART boundaries, and
4) extending the tolerable fault time with successful ART performance.
By applying the proposed ART-VS method, phase voltages are time-
varyingly regulated inside the dynamic boundaries introduced in the ART scheme,
leading to successful ride-through. The effectiveness of the proposed ART scheme
and ART-VS control method is validated by simulation and experimental test cases.
3.2 Overview of LVRT Codes in Different Countries
In the early 2000s, the LVRT requirements were initially mandated by grid codes
of the countries with high wind penetration levels such as Germany [65], Denmark
[75], Spain [76] and other European countries [77]-[78]. Grid code development in
other parts of the world usually follows Europe. In 2011, Chinese grid
code eventually mandated wind power plants to meet a set of interconnection
standards [79]. To increase the amount of wind generation and enhance grid
performance, China currently has plans to continuously update and improve its grid
30
code. In Canada, several interconnection requirements have been developed by
different transmission system operators [80]. In the United States, there are also
several regulatory institutions that study and shape national interconnection
standards, such as U.S. Federal Energy Regulatory Commission and
North American Electric Reliability Corporation. In compliance with these national
standards, regional reliability organizations have established their grid codes. Two
prominent examples are the projects conducted by Independent System Operator–
New England in 2009 [81] and the Electric Reliability Council of Texas in 2010
[82] which both have high wind installation targets for the future. As for the future,
more changes and improvements are expected for the grid codes in the
United States.
Typically, most grid codes require DG units to remain connected a minimum
of 150ms [80], during balanced and unbalanced faults. This period can,
however, vary based on the system characteristics (e.g., 400ms in Australian grid
code [72] and 625ms in Ireland grid code [78]) and different voltage sags
(e.g., 700ms in France grid code for voltage sags less than 0.5 p.u. [80]).
3.2.1 Reactive current injection (RCI)
The RCI under grid faults is another requirement identified by some grid codes to
provide the necessary support at the point of connection. In some countries, such as
Brazil with lower wind integration, the transmission system operator does not
stipulate yet the need of RCI during faults. However, system operators in some
countries (i.e., Germany [65], Denmark [75], England [77], Ireland [78], and Spain
[76]) impose RCI requirements for the large DG interconnections to support the
grid reliability under grid faults. The primary grid codes on LVRT [65], [75]-[78]
mainly focused on the interconnection requirements under balanced grid faults.
However, the most recent grid code, published in 2015 in Germany [83], has even
considered the negative-sequence current injection during unbalanced faults. In this
regard, recent studies [59], [84] have also proposed the new LVRT methods with
the negative RCI during unbalanced faults. These developments and continuous
updates in interconnection requirements and increasing demand for
31
high penetration of DGs clearly show the necessity of grid codes evolution into
more effective versions. The interconnection codes in different countries should
improve to achieve two crucial objectives at the same time:
1) increasing the penetration level of clean and renewable energy resources,
and
2) enhancing the stability and reliability of the highly-integrated grid.
This chapter thus proposes an extended version of the LVRT curves for the
proper operation of DG units under short-term unbalanced grid faults.
3.2.2 Frequency Control and Active Power Restoration
Frequency and active power control, under the grid faults, refer to the ability of DG
units to regulate their power output to a defined level either by disconnecting or
proper control [80]. The grid codes of Germany, Ireland, Nordic [86], and Denmark
demand DG units to have the ability of active power curtailment. Generally, most
grid codes require high capacity DG units to provide frequency response
and contribute to the regulation of system frequency. The Irish [78] and Danish [75]
codes demand active power control according to the frequency response curves.
According to the German code [65], DG units must reduce their active power with
a gradient of 40% (of the available power) per Hz when the frequency exceeds the
value 50.2 Hz. The British code requires wind power plants to supply primary and
secondary frequency control as well as over-frequency control. The Hydro-Quebec
grid code [90] requires the wind power plants (with rated power greater than 10
MW) to have a frequency support control system. The timeframe for active power
restoration varies in different grid codes. According to British [77] and Irish
[78] codes, the active power must be rapidly restored to at least 90% of the pre-
fault available value within 1s after the voltage recovery. While the German grid
code requires restoration with a rate at least equal to 20% of the nominal output
power (reaching 100% in 5s after voltage recovery) [65]. The requirement severity
on the active power restoration corresponds to the grid strength. For example, grid
codes in weak systems demand faster active power recovery to the pre-fault values
32
which is crucial for their system stability. It should be noted that the contribution
of this chapter is to propose advanced RCI requirements; and the active power
restoration and frequency control are not the main scope of this chapter. Therefore,
the timeframes of the active power restoration prescribed in the existing grid codes
can also be adopted by the proposed ART scheme in this chapter.
General schematic of the proposed ART boundary curves for the positive-sequence, negative-sequence, and phase-voltage magnitudes at the PCC of a DG unit.
3.3 Proposed Asymmetric Ride-Through (ART)
Guidelines
It is proposed in this paper to extend the LVRT curves by specifying certain
regulation curves for proper operation of DG units under short-term unbalanced
grid faults. In other words, the proper performance of DG units is defined in terms
of the three important voltage terms at the PCC using three proposed ART curves
illustrated in Fig 3.1. The first curve, named LBVP, defines a lower boundary for
the positive-sequence voltage value, Vp, (under unbalanced grid faults) that is
similar to the LVRT curves which typically define boundaries for the RMS values
of the voltage at the PCC. Therefore, five time parameters ( 51 2, ...,lp lp lpT T T ) and five
33
voltage parameters ( 51 2, ...,lp lp lpV V V ) have been embedded in the proposed LBVP
curve to be able to capture the specifications from 23 different grid codes [72]-[80].
For instance, only two lpT and two lpV parameters are enough to adopt the LBVP
curve of Fig 3.1 from the LVRT codes of Germany [65] and Ireland [78]. However,
adopting from some other codes requires more parameters. For instance, three lpT
and three lpV parameters are required to adopt LBVP curve from the French and
Italian codes [80].
The second proposed curve, named HBVN, defines a higher boundary for the
negative-sequence voltage value, Vn, at the PCC. The HBVN curve is important
since it prescribes DG units to support the grid by balancing the phase voltages and
reducing the negative-sequence component. To present a simple yet effective
boundary for the negative-sequence voltage, the proposed HBVN curve is designed
adaptive to the first curve, i.e., LBVP, as demonstrated in Fig 3.1. Thus, it only
comprises one time parameter ( 1hnT ) and two voltage parameters ( 1 2,hn hnV V ). The
third proposed curve, named HBVP, determines the higher boundary for the phase
voltage peaks at the PCC. This curve is beneficial to regulate the maximum
tolerable voltage magnitudes based on the system and DG unit characteristics and
avoid over-voltages. The HBVP curve is designed to be able to capture the
specifications of the over-voltage regulations in different codes. Thus, it has three
time parameters ( 1 2 3, ,hp hp hpT T T ) and four voltage parameters ( 1 2 4, ...,hp hp hpV V V ) as
shown in Fig 3.1.
As stated earlier, three proposed ART curves aim to extend the concept of the
existing LVRT curves to better regulate the operation of the grid-connected
converters under asymmetric short-term faults for increasing the reliability in
future’s highly integrated power systems. Therefore, the following requirements are
proposed in this chapter for a successful ART scheme, according to Fig 3.1:
1) Vp is (or can be regulated) above the LBVP curve
2) Vn remains (or can be regulated) under the HBVN curve, and
34
3) for unbalanced faults, none of the phase voltage magnitudes exceeds the
HBVP curve.
If the applied VSS in the grid-connected converter-based unit can satisfy all
three requirements, the unit can stay connected to the grid to avoid cascaded outages
and support the system reliability. Three proposed ART curves contain 11 voltage
parameters and 9 time parameters in total. These 20 parameters, not only, make the
ART scheme comprehensive and capable of adopting from the existing codes; but
also, provides a proper specific regulation for asymmetric faults. Therefore, each
grid code, based on its system characteristics and requirements, can suggest specific
ART curves similar (or in addition) to its already-established LVRT curve.
Based on the general curves of Fig 3.1, two examples of the ART curves are
proposed in this chapter. Fig 3.2 illustrates the first proposed curve, named ART-1,
which comprises two stages, i.e., withstanding (immediately after the fault) and
recovery stages. The duration of the first stage in the ART-1 is suggested to be
150ms after the fault occurrence. This value can vary based on the specification of
each grid. However, since most grid codes have the first stage duration of 150ms in
their LVRT curves, it is also suggested here for the ART-1 scheme. If the fault lasts
more than 150ms and one of the followings happens:
• the magnitude of the positive-sequence voltage goes under the LBVP curve,
or
• the magnitude of the negative-sequence voltage goes above the HBVN
curve, or
• one of the phase voltage magnitudes goes above the HBVP,
the DG has two options:
• disconnecting from the grid, or
• remaining connected to the grid and supporting the PCC voltage (as much
as it can) to satisfy the ART requirements.
35
Here, the goal is to keep the voltage magnitudes within the prescribed
boundaries of the ART scheme as much as possible by boosting the positive-
sequence voltage and reducing the negative-sequence value. Without any support,
when one of the voltage terms passes the corresponding ART curve, it is no longer
necessary to stay connected; but it is still preferred that the DG utilizes its available
capacity to further stand connected by regulating its voltage parameters within the
prescribed ART boundaries. The more one DG can support the PCC to stay within
the prescribed ART boundaries, the more reliability the host grid can have. For the
simplicity, 20 ART parameters of Fig 3.1 are aggregated in six voltage parameters
and three time parameters (as shown with the suggested values in Fig 3.2). Fig 3.3
also shows another proposed example for riding through asymmetrical faults,
named as ART-2. According to ART-2 curves, the faults with Vp down to zero
should be tolerated up to 150ms. Also, the voltage sags with a Vp value more than
0.5p.u. should be endured up to 2s. The values of eight voltage parameters and four
time parameters in ART-2 curves are proposed as shown in Fig 3.3.
Proposed ART-1 curves.
36
Proposed ART-2 curves.
3.4 Overview of Conventional Voltage Support Strategies
under Unbalanced Conditions
This chapter overviews the VSSs under unbalanced conditions, presented in the
recent works [36]-[53]. These strategies are categorized into four groups and briefly
discussed. The compliance of the reviewed four VSS groups [36]-[53] with the
proposed ART scheme is studied in section 3.5.
Fig 2.1 illustrated the diagram of a DG unit interfaced with a grid-connected
converter. For any unbalanced condition, the positive and negative sequence
voltage vectors can be written in the αβ frame as
cos( t ) cos( t )
,sin( t ) sin( t )
v vV Vv v
v vV Vα α
β β
ω δ ω δ
ω δ ω δ
+ −+ + − −+ −
+ −+ + − −
+ += = = =
+ − + (3.1).
To exploit a flexible and supportive performance from a DG unit, its injected
reactive current vector, iq, can be divided into positive and negative sequences as
p q qi i i i+ −= + + or
37
cos ( )
sin ( )
sin ( ) sin ( )
cos ( ) cos ( )
p
p
q q
q q
I tii
i I t
I t I t
I t I t
α
β
ω δ
ω δ
ω δ ω δ
ω δ ω δ
+
+
+ + − −
+ + − −
+ = = + + − + + + − + − +
(3.2),
where the superscripts “+”/“-” and subscripts “p”/”q” denote the positive/negative
and active/reactive components, respectively. The mathematical expressions of the
ac-side voltages are
g gg g
g g
v vv v i idv v v L Rdtv v i iv v
α αα α α α
β β β ββ β
+ −+ −+ −
+ − + −
= + = + = + + +
(3.3),
where the subscript “g” represents the grid components. In the following sub-
sections, different voltage support techniques introduced in the literature [36]-[53]
for DG units under unbalanced conditions are presented in four categories.
3.4.1 Positive-Sequence Reactive Current Injection (PSRCI)
The German grid code, E.ON [65] forces wind farms to support grid voltage with
additional reactive current only during a three-phase symmetrical voltage dip,
amounting to at least 2% of the rated current for each percent of the voltage dip.
The symmetrical voltage dip is defined as the magnitude of the balanced three-
phase voltage drop at the low-voltage side of the interconnection transformer.
Similarly, references [36]-[39] tried to present some strategies to apply this rule in
the case of asymmetrical faults. Therefore, the reference value for the reactive
current, , can be generated by [65]
max, 2 nom prefq PSRCI
nom
V VI I
V+−
= × × (3.4),
where Vnom is the nominal voltage, and Imax is the rated current of the inverter.
38
3.4.2 Voltage Support Based on the Maximum Allowable Reactive
Power Delivery (MARPD)
The grid codes in Britain [77] and Ireland [78] denote that wind power plants must
deliver their maximum reactive current only during a symmetrical voltage dip.
Similar to Britain and Ireland grid codes [77]-[78], references [41]-[42] presented
the MARPD for unbalanced grid conditions. Using the MARPD strategy, the GSI
injects the maximum reactive power and respects the phase currents limit under
unbalanced faults by reactive current command of
2 2max,
refpq MARPDI I I+ = − (3.5),
where Ip is the reference value of the active current. The detailed derivation of
maximum available reactive currents can be found in [41]-[42].
3.4.3 Mixed Sequence Injection (MSI)
References [43]-[45] suggested some strategies which are based on the injection of
both positive and negative currents to support the connection voltage by a
combination of boosting and equalizing the phase voltage magnitudes. According
to [44], both positive and negative sequence reactive currents are injected under
unbalanced faults. The reference values for Eq (3.2) can thus be obtained as
1 2max max, ,,pref ref n
q MSI q MSInom nom
V V V VI k I I k IV V
+ −+ −
− −= × × = × × (3.6),
where the recommended values for four parameters of (6) are , p.u., and p.u. [44].
3.4.4 Positive-Negative Sequence Voltage Regulation (PNVR)
In the most recent literature [46]-[53], the voltage regulation strategies aim to
determine proper reactive current reference values to regulate the phase voltage
magnitudes within the desired margin under unbalanced conditions. The
magnitudes of the phase voltages in terms of the magnitudes of positive
and negative sequence voltages are obtained by the following expressions:
39
( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) ( )
2 2 0 0
2 2 0 02 23 3
2 2 0 02 23 3
2 cos cos
2 cos cos cos
2 cos cos cos
a p n p n
b p n p n
c p n p n
V V V V V V
V V V V V V
V V V V V V
π π
π π
γ φ
γ γ φ
γ γ φ
= + + +
= + + − + +
= + + + + −
(3.7),
where Va, Vb, and Vc are magnitudes of the phase voltages, and γ δ δ+ −= − ,
0 0γ δ δ += − . References [46]-[51] neglect the zero sequence voltage terms and
simplifies the problem. Then, the reference values for the positive and negative
voltage values are obtained in [49] as
( ) ( ) ( )( )
2 22 2 2 2 2 22
2y x y x y x
ref
xV yV xV yV V VV
x y+
− + − − −=
−
( ) ( ) ( )( )
2 22 2 2 2 2 22
2y x y x y x
ref
xV yV xV yV V VV
x y−
− − − − −=
− (3.8),
where,
{ } { }( )
( ) ( ) ( )( )( ) ( ) ( )( )
min
max min
2 23 3
2 23 3
,
min , max , , min , ,
min cos ,cos ,cos ,
max cos ,cos ,cos
y
x a b c a b c
V V
V V V V V V V V V
y
x
π π
π π
γ γ γ
γ γ γ
=
= + −
= − +
= − +
(3.9).
Finally, the reference values of Eq (3.10) are determined:
, ,( ) , ( )ref refref g g g ref gq PNVR q PNVRI V V X I V V X+ + − −
+ −= − = − (3.10),
where Xg is the equivalent line impedance (i.e. g gX Lω= ). Eq (3.10) provides the
voltage regulation based on the positive and negative sequence voltage values, and
it is named PNVR in this chapter. The positive and negative reactive currents that
fulfill the voltage support method need an estimate of the line inductance. In [46],
[49], the PNVR strategy was only applied to the STATCOM application where
40
the reference current only consists of the reactive components. Also, the PNVR
strategy is only suggested for the inductive grids. However, the effects of the
inverter active power and line resistance in regulating the voltage are considered in
[52].
3.5 Compliance of the Conventional Voltage Support
Strategies with the Proposed ART Guidelines
This section examines the capability of the conventional voltage support techniques
[36]-[53] in satisfying the ART requirements. The test system is shown in Fig 2.1
(with the parameters listed in Table 3.2). To demonstrate the performance of these
strategies considering the proposed ART requirements, a short-term unbalanced
(double-phase) fault of Fig 3.4 is implemented. According to ART-1 with =1s, the
DG is required to withstand at least 0.75s after the fault occurrence since all three
criteria are met until this time (see Fig 3.4(a)). After 0.75s, it is preferred that the
DG utilizes its available capacity to further stand connected by regulating its
voltage parameters within the ART boundaries. If the ART-2 scheme is imposed in
this case, the DG is only required to withstand the unbalanced fault up to 150ms
after the occurrence since the positive voltage goes to the area where disconnection
is allowed by ART-2 (see Fig 3.4(b)). However, it is preferred that the DG uses a
proper technique to regulate the voltage terms within the ART curves.
41
(a)
(b)
Test Case A: two-phase fault scenario when (a) ART-1 scheme, or (b) ART-2 scheme is applied.
42
(a)
(b)
Test Case A: ART-1 scheme with conventional VSSs: (a) PSRCI [36]-[39], (b) MARPD [41]-[42].
43
(a)
(b)
Test Case A: ART-1 scheme with conventional VSSs: (a) MSI [43]-[45], and (b) PNVR [46]-[53].
44
Fig 3.5 and 3.6 demonstrate the performance of the four conventional VSSs
under the unbalanced condition of Fig 3.4 when the ART-1 scheme is imposed.
According to Fig 3.5, none of the strategies can fully ride-through the unbalanced
fault until the fault clearance. As expected, Fig 3.5(a) shows that the PSRCI
strategy only supports the positive sequence voltage. This strategy suffers from the
lack of negative-sequence reactive current injection. Therefore, the un-faulted
phase experiences an overvoltage, there is a high unbalance between the phases,
and the negative sequence voltage remains high. According to Fig 3.5-(b),
the MARPD strategy has an almost similar performance. As expected, the MARPD
strategy uses all the reactive current capacity and causes a higher boost in all phases
in comparison with the PSRCI results. Not only this higher reactive current does
not help the voltages properly but also it worsens the situation by creating higher
overvoltage in the un-faulted phase. As Fig 3.6-(a) shows, although the negative
and positive sequence voltages are appropriately controlled by the PNVR, this
strategy is not successful in avoiding the overvoltage on the un-faulted phase. The
MSI has better results than the other three strategies, as indicated in Fig 3.6-(b). All
phase voltages stay under the ART-1 boundary, and the positive sequence voltage
is compensated above the proposed boundary until 1.1s after the fault. Therefore,
the MSI is the only strategy that could regulate the voltage terms within the
recommended boundaries more than 0.75s (which is the required time imposed by
the ART-1 for this fault case).
Proposed ART-VS dynamic reference setting for Vmax and Vmin.
45
Proposed ART-VS control blocks.
3.6 Proposed ART-Adaptive Voltage Support
As examined in the previous section, the existing VSSs in the literature are not able
to completely fulfill the three criteria proposed in the ART scheme. Sometimes they
fail before the required time of staying connected, and sometimes they do not have
preferable performance after the required time. Therefore, an advanced voltage
support method is proposed in this chapter, named ART-VS. The proposed ART-
VS method has two significant advantages:
1) it is adaptive to the proposed ART curves, and
2) its reference values (for the phase voltage magnitudes) can dynamically
vary during and after the fault to provide the superior voltage regulation
and riding-through capabilities.
The proposed adaptive and dynamic setting of the reference values for the
minimum and maximum phase voltage magnitudes are based on the
system characteristics, and they dynamically change during the ART period as
46
illustrated in Fig 3.7. This setting consists of four parameters, Vmin-1, Vmin-2, Vmax-1,
and Vmax-2. These parameters can be determined based on the system characteristics:
1) line impedance, Xg,
2) type, depth, and duration of the worst unbalanced fault that is needed to
be ridden through, and
3) peak currents of the power electronic switches.
The grid voltage is estimated by the local measurements and using the
following equation:
g g gdiv v R i Ldt
= − − (3.11).
3.6.1 Determination of Dynamic Reference Values for Minimum
and Maximum Phase Voltage Magnitudes
In the proposed ART-VS method, the desired operation is to regulate the all three-
phase voltage magnitudes such that the minimum and maximum phase voltage
magnitudes, Vmin and Vmax, are dynamically regulated adaptive to the proposed ART
curves. If the rated power of the DG unit and the connecting line impedance are not
small, this objective can be accomplished by reference values indicated in Fig 3.7
for Vmin and Vmax. For example, in the studied case of the previous section, where
Xg=0.5 p.u. and Imax=1 p.u., the four parameters of Fig 3.7 can be pre-determined
as follows.
Determination of Vmin-1:
The following equation shows how much boost in one phase is expected
based on the reactive current injection in that phase and the line impedance.
, : , , ,i i qV XI i faulted phase a b or c∆ = (3.12).
Therefore, if the maximum current limit is assumed 1 p.u. and X is 0.5p.u. the
following voltage boost in the faulted voltage can be expected:
, min 10.5 . . 0.5 . .i i q iV XI p u V V p u−∆ ≤ = → − ≤ (3.13).
47
From Eq (3.13) and considering the demand of the ART-1 scheme which is
tolerating the unbalanced faults even down to the zero at the withstanding stage (see
Fig 3.1), a proper Vmin-1 can be selected as
min 1 0.5 . .V p u− ≤ (3.14).
Determination of Vmax-1:
Utilizing the negative reactive current in Eq (3.2), the overvoltage on the un-
faulted phase can be avoided; and simultaneously, the negative sequence voltage
and unbalance factor can be reduced by proper setting of Vmax-1. Therefore, the
maximum reduction on un-faulted phase can be formulated, and Vmax-1 can
be determined as
j, max 1| | 0.5 . . 0.5 . .j q jV XI p u V V p u−∆ ≤ = → − ≤ (3.15).
j : , , ,unfaulted phase a b or c
In the normal cases, the un-faulted phase voltage is typically 1 p.u.. Thus,
max 10.5 . . 1 . .p u V p u−≤ ≤ (3.16).
Determination of Vmax-2 and Vmin-2:
Depending on the selected ART scheme, the value of Vmax-2 and Vmin-2 are
determined. For example, for the ART-1 and ART-2 schemes presented in Figs. 2
and 3, Vmax-2 and Vmin-2 are obtained 1.1p.u. and 0.9p.u., respectively. Also, for the
simplicity, the following expression can be set
min 2 min 1 max 2 max 1V V V V− − − −− = − (3.17).
Then, Vmin-1 and Vmax-1 can be found based on (14), (16), and (17). For
example, if Vmin-1=0.5p.u. is chosen from Eq (3.14), Vmax-1 is obtained 0.7p.u. based
on (3.17) and the values of Vmax-2=1.1 p.u. and Vmin-2=0.9p.u..
48
3.6.2 Reactive Current Injection
The dynamic reference values of minimum and maximum phase voltage
magnitudes, minrefV and max
refV , that are introduced in the previous sub-section and
shown in Fig 3.7, are used to calculate the proper dynamic set-points for the
proposed ART-VS method. From (3.7), the maximum and minimum phase
voltage magnitudes can be determined by
( ) ( ) ( )( ) ( )
( ) ( ) ( )( ) ( )
2 2 0 0min min
2 2 0 0max max
2
2
V V V V V y V
V V V V V x V
λ
λ
+ − + −
+ − + −
= + + +
= + + + (3.18),
where 0minλ and 0
maxλ can be found as follows
( ) ( )( ) ( )
0 02 21 min 13 3
0 02 22 max 23 3
cos cos
cos cos
if y k k
if x k k
π π
π π
γ λ γ
γ λ γ
= + → = +
= + → = + (3.19),
where k1 and k2 can take 0, 1, and -1 values, respectively, for phases a, b, and c.
Applying minrefV and max
refV from Fig 3.7 in (3.18), the dynamic values for the refV + and
refV − can be solved. It is worth mentioning that Chapter 4 discusses solving the refV +
and refV − equation while considering the zero-sequence compensation.
Finally, the required reactive current references in the proposed ART-VS
method can be set as
, ,,ref g g refref refq ART VS q ART VS
g g
V V V VI I
X X
+ + − −
+ − − −− −
= = (3.20).
3.7 Simulation Results
As presented in section 3.5, none of the four conventional voltage support groups
could fully ride through the asymmetric fault of test case A. However, the proposed
ART-VS method provides the adaptive and dynamic voltage regulation. As Fig 3.9
illustrates, the ART-VS method regulates the values of Vp, Vn, and phase voltage
49
magnitudes within the ART-1 boundaries and satisfies all three requirements
presented in section 3.3. Therefore, the DG unit experiences a successful ride-
through under this unbalanced fault. To further show the effectiveness of the
proposed ART-VS method, four other simulation test cases are examined in this
section. The fault characteristics of all test cases are reported in Table 3.1. Table
3.4 presents the results of the conventional strategies and the proposed ART-VS
method. According to this table, the PSRCI and MARPD strategies suffer from the
lack of negative voltage support. Furthermore, the PNVR and MSI strategies show
better performances. According to TABLE 3.3, the MSI gives proper results in
regulating the phase voltage peaks and insufficient performance in reducing the
unbalance factor. On the other hand, the PNVR is successful in reducing the
negative-sequence voltage and ineffective in regulating the peak values. Thus, these
two strategies are unable to fully satisfy the three requirements defined by the ART-
1 scheme. In contrast, the proposed ART-VS method successfully satisfies all three
requirements in all cases.
Fig 3.10 shows the comparison between the results of the PSRCI and ART-
VS strategies under the time-varying asymmetric fault of the test case E. In this test
case, both faulted phases experience time-varying voltage dip. As Fig 3.10(a)
shows, the phase voltage of the un-faulted phase, in the PSRCI strategy, exceeds the
HBVP boundary. However, Fig 3.10(b) shows that the ART-VS method satisfies
the three requirements and provides the successful ART performance.
TABLE 3.1 Fault Characteristics of Five Test Cases
Faulty phases (p.u.) Vp (p.u.) Vn (p.u.)
Test Case A Va = Vb = 0.1 0.4 0.3
Test Case B Va = 0 0.67 0.33
Test Case C Va = Vb = 0 0.33 0.33
Test Case D Va = 0, Vb = 0.5 0.5 0.29
Test Case E Va(t) = -0.5t+0.6
Vb(t) = 0.75t+0.1 Vp(t) = 0.08t+0.57
50
Test Case A: Voltage support by the proposed ART-VS.
TABLE 3.2 Simulation Test System Parameters
Zg j0.48 Ω VDC 1500 V
S 1.0 MVA VL-L, RMS 690 V
Imax 200 A f 60 Hz
TABLE 3.3 Experimental Test System Parameters
Imax 20 A (peak) Vg 208 V
Lg 2.7 mH f 60 Hz
Vmin-1 125 V Vmin-2 187 V
Vmax-1 166 V Vmax-2 229 V
1hnT 0.5 s 2
hnV 2 V
51
(a)
(b)
Test Case E: voltage support results by (a) conventional PSRCI strategy and (b) proposed ART-VS method.
52
TABLE 3.4 Results of the Four Conventional Voltage Support Techniques [36]-[53] and the Proposed ART-VS Method
Strategy LBVP HBVN HBVP
Test Case B
PSRCI ×
MARPD - × ×
MSI -
PNVR ×
ART-VS
Test Case C
PSRCI × -
MARPD × ×
MSI ×
PNVR ×
ART-VS
Test Case D
PSRCI × -
MARPD × ×
MSI -
PNVR ×
ART-VS
Test Case E
PSRCI - ×
MARPD - × ×
MSI ×
PNVR ×
ART-VS
53
3.8 Experimental Results
To further verify the effectiveness of the proposed schemes, a laboratory-scale test
system is also employed. The test system contains a voltage source converter
connected to an ac grid via impedances and a transformer. A Semistack intelligent
power module, shown in Fig 3.11, is used which includes gate drives, six insulated-
gate bipolar transistors, and protection circuit. The switching frequency of the
transistors is 10 kHz, showing the computational efficiency of the proposed control
technique. The converter is controlled by a dSPACE1104 card via a CMOS/TTL
interfacing circuit, and is connected to a 60-Hz, 110-V (phase-voltage) grid.
The software code is generated by using the Real-Time Toolbox under a
MATLAB/Simulink environment for PWM signals generation. The parameters are
listed in Table 3.3. The unbalanced faults are realized using circuit breakers and
different fault impedances for each phase, as indicated for the without support case
in Fig 3.12. Fig 3.13 and Fig 3.14, respectively, show the results of the conventional
MSI strategy and the proposed ART-VS method, under the fault indicated in Fig
3.12. Bottom figures in Fig 3.13 and Fig 3.14 indicate the reference values of the
positive- and negative-sequence reactive currents obtained by the MSI and ART-
VS strategies. As Fig 3.13 reveals, the MSI method fails to satisfy the first two
recommendations in the ART-1 scheme. However, the ART-VS method
demonstrates successful performance in terms of all three criteria of the ART-1
scheme as indicated in Fig 3.14.
54
Scaled-down test setup.
Experimental Test: without support.
55
Experimental Test: (a) voltage without support, (b) voltage and current components with MSI,
56
Experimental Test: voltage and current components with proposed ART-VS
3.9 Discussion
The proposed ART curves in section 3.3 can be prescribed for any type of DG
units including converter-interfaced distributed energy resources (e.g., permanent
magnet synchronous generators or photovoltaic), directly-connected generating
units (e.g., squirrel cage induction generators), or doubly-fed induction generators.
Although the main application of the proposed ART curves is high capacity wind
power plants, they can be implemented for DG units with any energy resource such
as wind, solar, wave, geothermal, etc. The proposed curves can also be imposed for
the proper operation of HVDC systems and grid-interactive microgrids.
57
Furthermore, the proposed ART-VS method in section 3.6 can be applied to any
converter-interfaced applications such as different types of converter-interfaced DG
units [41]-[42], grid-interactive converter-interfaced microgrids [59], and
converter-interfaced HVDC systems [44]. Since the voltage support in most cases
is obtained using the reactive current, the nature of the energy source (that
is responsible for generating the active power) does not affect the effectiveness of
the proposed ART-VS method. To fulfill the ART-VS method, it is needed to
estimate the line impedance. This impedance can be estimated online [87]-[89]; and
be updated inside the proposed ART-VS control loops. Also, the equivalent grid
voltage can be simply obtained by a Kirchhoff voltage law equation and local
measurements. Since a symmetrical fault can be considered as a simple case of the
generic asymmetrical conditions (with the negative-sequence voltage value equal
to zero), all analyses in this chapter remain intact. The proposed ART curves and
ART-VS control method can thus be simply applied under the three-phase grid
faults.
The specification on the active power limitation during the fault and its
restoration after the fault is an important area which needs similar comparative
research. These specifications vary in different grid codes based on system
characteristics such as grid strength. Although the imposed specifications on active
power restoration by different grid codes can be adopted by the proposed ART
regulation scheme, it is an interesting area for future research on specific
requirements of active power restoration (from the system operator point of view)
under unbalanced grid faults.
3.10 Conclusion
This chapter presented three contributions. First, the LVRT along with the reactive
current injection and active power restoration requirements in different grid codes
were overviewed. Also, the existing voltage support strategies in the literature,
under unbalanced grid faults, were reviewed and categorized. Second, the LVRT
curves were extended for short-term unbalanced faults, and the asymmetric ride-
58
through (ART) curves were proposed. The ART scheme prescribes
proper specifications on the regulation of the phase voltage magnitudes and the
positive- and negative-sequence voltages. This chapter showed that even the most
recent voltage support strategies in the literature are not able to fully comply with
the suggested ART specifications. As a third contribution, a new dynamic
and adaptive voltage regulation method was proposed, named ART-adaptive
voltage support. The proposed adaptive voltage support method helps the
connection voltage under any unbalanced voltage sag by
1) regulating all phase voltages inside the ART boundaries within the
dynamic margins,
2) boosting the positive-sequence voltage value,
3) reducing the voltage unbalance factor, and
4) being adaptive to different grid codes.
The results of the proposed ART scheme and ART-adaptive voltage support
were successfully verified by simulation and experimental test cases.
59
Chapter 4
Advanced Asymmetric Voltage
Regulation and MAS Scheme in A Single
Grid-Interactive Smart Inverter
4.1 Introduction
This chapter proposes a MAS scheme with an advanced asymmetric voltage
regulation strategy. Under most grid faults, the accuracy of the traditional VSSs
is severely affected due to the existence of the zero-sequence voltage component.
References [47]-[48] aim to regulate the positive and negative sequences of the
PCC voltage. However, it is more desirable to control the phase voltage magnitudes
[46], [49]. Conventional VSSs under unbalanced conditions [46]-[51] generally
suffer from three drawbacks:
1) none of them considers the zero-sequence voltage component.
2) the methods presented in [47]-[49] have been studied only in
the STATCOM applications where the active power is assumed zero.
3) the methods suggested in [46], [48]-[50] have been only applied in inductive
grids, i.e., assuming very high X/R ratio.
60
Therefore, this chapter proposes an advanced VSS in a GSI unit, called zero-
sequence compensated voltage support (ZCVS) to address the aforementioned three
issues. It has the following advantages compared to the existing VSSs:
1) It fully compensates the zero-sequence component and accurately
regulates the phase voltages within the pre-set safety limits under
unbalanced fault conditions. The safety voltage limits are
typically imposed by grid codes for uninterrupted operation of GSIs.
2) Unlike most of the traditional methods, the proposed ZCVS is adapted
with any complex grid impedance, e.g. resistive and inductive
distribution systems.
3) The active power transferred by the GSI is also considered. The MAP
equations for the ZCVS is also formulated. Therefore, this technique can
be considered as a MAS scheme.
The delivered active power may, however, become highly oscillatory under
severe unbalanced conditions. This chapter also proposes an analytical technique to
limit the active power oscillations (LAPO) and enhance dc-bus voltage stabilization
while, simultaneously, the GSI is supporting the ac host grid. Both of the last two
strategies, i.e., MAP and LAPO, can be simultaneously augmented to the proposed
ZCVS strategy.
4.2 Proposed Zero-sequence Compensated Voltage
Support (ZCVS) Scheme
The basic requirement in the voltage support is to avoid the over-voltage and under-
voltage at the PCC whenever possible. Eq (3.3) can be expanded as
61
( ) ( )( ) ( )( ) ( )( ) ( )
cos( t ) cos( t )
sin( t ) sin( t )
cos ( ) cos ( )
sin ( ) sin ( )
g g
g g
g q g p g p g q
g q g p g p g q
V V V V
V V V V
L I R I t R I L I t
L I R I t R I L I t
ω δ ω δ
ω δ ω δ
ω ω δ ω ω δ
ω ω δ ω ω δ
+ + + − − −
+ + + − − −
+ + + − − −
+ + + − − −
− + + − + = − + − − + + + + − + + + − − +
(4.1),
where δ + and δ − are angles of the positive and negative sequences of the voltage.
If the following expressions are satisfied:
,p g p g
g gq q
I R I RL LI Iω ω
+ −
+ −= = − (4.2);
then, the positive and negative components of (4.1) result in
,g g q g p g g p g qV V L I R I V V R I L Iω ω+ + + + − − − −− = + − = − (4.3).
To comply with voltage limits, a combination of positive/negative and
active/reactive currents (i.e., pI + , pI − , qI + , and qI − ) should be injected into an
inductive-resistive grid to support the grid voltage. The magnitudes of the phase
voltages can be obtained in terms of the magnitudes of positive and negative
sequence voltages by Eq (3.7). From Eq (3.7), the maximum and minimum phase
voltages with zero-sequence consideration can be determined by
( ) ( ) ( )( ) ( )
( ) ( ) ( )( ) ( )
2 2 0 0min min min
2 2 0 0max max max
min( , , ) 2
max( , , ) 2
a b c
a b c
V V V V V V V V V
V V V V V V V V V
λ λ
λ λ
+ − + −
+ − + −
= = + + +
= = + + + (4.4),
where minλ , maxλ , 0minλ , and 0
maxλ can be found as follows:
( )( )( )
min23
max23
cosmin( , , )
cosmax( , , )
cos
aa b c
ba b c
c
π
π
λ γλ λ λ λ
λ γλ λ λ λ
λ γ
= = = − → = = +
62
( )( )( )( )( )( )
0 0min min
0 0 2min min 3
0 0 2min min 3
0 0max max
0 0 2max max 3
0 0 2max max 3
cos
cos
cos
cos
cos
cos
a
b
c
a
b
c
if
if
if
if
if
if
π
π
π
π
λ λ λ γ
λ λ λ γ
λ λ λ γ
λ λ λ γ
λ λ λ γ
λ λ λ γ
= → = = → = −
= → = + = → = = → = −
= → = +
(4.5),
where γ δ δ+ −= − and 0 0γ δ δ += − . After applying proper minrefV and max
refV in (4.4), the
reference values of refV + and refV − can be solved as
( )
( )
2 22
max min
max0 0 2
min min0 0 2
max max
4 ,2
22
( )
( )
ref refref
H L
Href
Lref
H
B B A AV VV
V VA
B A VV V VV V V
λ λλ
λ
λ
+ −+
− + −= =
− = − = × − = − = −
(4.6).
A general solution (applicable in grids with any X/R ratio) is to apply the
results of (4.6) in (4.3) as
2 2 2 2
2 2 2 2
, ,
,
g gp ref p ref
g g g g
g gq ref q ref
g g g g
R RI V I V
X R X R
X XI V I V
X R X R
+ + − −
+ + − −
= ×∆ = ×∆+ +
−= ×∆ = ×∆
+ +
(4.7),
where expressions of (4.2) are also satisfied. According to (4.7), the active
components do not contribute in supporting the voltage in an inductive grid. In this
case, they can be utilized to fulfill complementary objectives discussed in the next
section (i.e., MAP strategy). Fig 4.1 shows the control diagram of the proposed
ZCVS scheme.
63
4.3 Proposed Complementary Strategies
For an inductive grid, the positive and negative sequences of the reactive
current component were obtained for regulating the phase voltages. In this section,
two complementary strategies are proposed to be applied to the active components
of the current. These strategies can be also obtained for the resistive grids and grids
with any X/R value if the active and reactive components are replaced or (4.2) is
satisfied.
4.3.1 ZCVS with LAPO Strategy
In severe unbalanced conditions, the required negative reactive component of the
current obtained by ZCVS may become high. Negative-sequence current and
voltage components give rise to large oscillations in the active power. Therefore,
the LAPO strategy is proposed to obtain a limit for the negative reactive current
component which prevents exceeding the pre-set maximum allowable active power
oscillation. Using the instantaneous power theory, the output active and reactive
powers of the GSI is calculated by Eq (2.3). Using Eq (2.3) gives the magnitude of
the oscillations on the active power as
( ) ( )2 2
p p q qP V I V I V I V I− + + − − + + −= + + − (4.8).
Proposed voltage support scheme
64
Using (4.8), the equation of the maximum negative reactive current can also
be obtained which limits the oscillation magnitude of the active power to the pre-
set value:
( )22max
,
setp p q
q LAPO
P V I V I V II
V
− + + − − +−
+
− + +=
(4.9).
Fig 4.2 shows the control diagram of the ZCVS scheme with LAPO strategy.
LAPO may slightly affect the operation of the ZCVS. However, the GSI operator
can flexibly compromise between the full ZCVS and the limited oscillation on
active power, by using these analytical expressions.
Proposed control diagram to limit the active power oscillations
4.3.2 ZCVS with MAPD Strategy
Augmenting the MAPD technique to ZCVS method ensures four simultaneous
objectives: i) riding through abnormal conditions, ii) regulating the phase voltages,
65
iii), delivering the maximum allowable active power to the grid and iv) respecting
the current limitations. This section finds the MAPD equation to achieve the
aforementioned goals in an inductive grid. In this strategy, qI + and qI − are already
obtained by (4.7) to provide the proposed voltage support. The value of pI − is also
set to zero in order to allocate all the available current capacity to pI + . Then, (2.5)
can be rewritten as
( ) ( )( ) ( )
sin cos ( ) cos sin ( )
sin sin ( ) cos cos ( )
p q q q
p q q q
I I t I I tii I I t I I t
α
β
γ ω δ γ ω δ
γ ω δ γ ω δ
+ − + + − +
+ − + + − +
+ + + − + = − + − + +
(4.10).
The αβ currents of (4.10) are transformed into the abc currents, and the
magnitude of the phase currents will be obtained as
2 22a2 2 23 31 1b 2 2 2 22 2 23 31 1c 2 2 2 2
( ) ( )
( ) ( )
( ) ( )
c s
c c s s
c c s s
I II
I I I I I
I I I I I
α α
α β α β
α β α β
+ = − + + + − − + −
(4.11),
where
( )sin , cos , sin , cosc p q s q q s p q c q qI I I I I I I I I I I Iα α β βγ γ γ γ+ − + − + − + −= + = − = − = − +
(4.12).
Then, the phase current magnitudes under the fault can be found by
( ) ( )2 22a sin cosp q q qI I I I Iγ γ+ − + −= + + − ,
( ) ( )222 31b 1 22 2p Q p QI I I I I+ += + + + ,
( ) ( )222 313 42 2c p Q p QI I I I I+ += + + − + (4.13),
where
66
3 311 2 2 2
31 12 2 2 2
sin cos
cos sin
Q q q q
Q q q q
I I I I
I I I I
γ γ
γ γ
− + −
+ − −
= + +
= − + −
3 31
3 2 2 2
31 14 2 2 2
sin cos
cos sin
Q q q q
Q q q q
I I I I
I I I I
γ γ
γ γ
− + −
+ − −
= − −
= − + + (4.14).
Using Eq (4.11)-(4.14), three values are respectively obtained for pI + ( ,p aI + ,
,p aI + , and ,cpI + ) in three cases, i.e., Ia= maxsetI , Ib= max
setI , and Ic= maxsetI :
( )22, max cos sinset
p a q q qI I I I Iγ γ+ + − −= − − −
( ) ( )2 2 2 21 2 1 2 1 2 max
,
3 3 4
2
setQ Q Q Q Q Q
p b
I I I I I I II +
− − + + − + −=
( ) ( )2 2 2 23 4 3 4 3 4 max
,c
3 3 4
2
setQ Q Q Q Q Q
p
I I I I I I II +
− + + − − + −=
( ), , , ,cmin , ,p MAPD p a p b pI I I I+ + + += (4.15).
Fig 4.3 shows the control diagram of the ZCVS scheme with MAPD strategy.
67
Proposed control diagram to maximize the active power delivery
4.4 Simulation Results
To demonstrate the effectiveness of the proposed ZCVS scheme with LAPO and
MAPD strategies, three test cases are studied and implemented in this section. The
test system is similar to the one studied in the previous chapter. To avoid the
simplicity assumption of the constant dc voltage source and realistically emulate a
renewable energy resource, the dc voltage regulator is also used in this chapter, and
the dc-link voltage controller generates the active power command of the GSI.
68
(a)
(b)
Simulation test case A: (a) magnitudes of the grid phase voltages, and (b) obtained positive and negative reactive currents by TVSS and ZCVS.
4.4.2 Test Case A: Traditional VSS vs Proposed ZCVS Method
Fig 4.4(a) shows six different unbalanced faulty conditions. Fig 4.4(b) indicates the
obtained qI + and qI − by the traditional VSS (i.e. TVSS) and proposed ZCVS for
different fault conditions. As Fig 4.5(a)-left reveals, TVSS fails to precisely
regulate the phase voltages within the pre-set voltage limits. Over-voltages up to
1.18 pu and under-voltages down to 0.83 pu occur whereas the voltage accepted
limits are set to ±0.1 pu around the nominal value. However, the proposed ZCVS
method demonstrates successful results. As Fig 4.5(a)-right shows, the phase-
69
voltages of the PCC are precisely regulated between the minsetV and max
setV . Also, it is
notable from Fig 4.5(d) that the dc voltage ripples are also considerablly lower
when the ZCVS is applied.
4.4.3 Test Case B: ZCVS with LAPO and MAPD strategies
First, the result of the ZCVS method with LAPO strategy is presented. The
maximum acceptable oscillation on the active power is set to 0.08 pu as indicated
in Fig 4.6(c). The maximum negative reactive current reference value is calculated
where the active power oscillations are lower than 0.08 pu. As Fig 4.6(a)
demonstrates, the reference value calculated is higher than ,q LAPOI − . It causes active
power oscillations greater than 0.08 pu as depicted in Fig 4.6(c). To limit the
oscillations, the reference value is limited to ,q LAPOI − at t=0.5s and t=0.9s, as indicated
in Fig 4.6(a). Therefore, the active power oscillations are limited to 0.08 pu as
shown in Fig 4.6(c). As a result, the dc voltage ripples are decreased too by applying
the LAPO strategy.
As another complementary strategy, the ZCVS method with MAPD strategy
is also tested in this section. The value of maximum phase current is set to 1.0 pu.
The suitable Ip is calculated. Fig 4.7(a) shows that an unbalanced fault occurs at
t=0.3s. The pre-fault active power is 1 p.u. which causes overcurrent as Fig 4.7
illustrates. At t=0.5s the chopper in the dc-side is activated to avoid the overcurrent
and the delivered active power becomes zero, as indicated in Fig 4.7(f). At t=0.7s,
the active current component obtained by proposed method is applied. Thus, the
MAPD strategy allows delivering maximum allowable active power (Fig 4.7(f))
while simultaneously respects the phase current limit (Fig 4.7(e)). As Fig 4.7(b)
shows, the ZCVS is still operating accurately even if the MAPD strategy is applied.
70
(a)
(b)
(c)
(d)
Simulation results of the traditional (left) and proposed (right) voltage support methods: (a) magnitudes of the PCC voltages, (b) phase currents, (c) active/reactive powers,
and (d) dc voltage.
71
(a)
(b)
(c)
(d)
Simulation results of ZCVS with LAPO strategy: (a) obtained positive and negative reactive currents by ZCVS and LAPO, (b) phase currents, (c) active power, and (d) dc voltage.
72
(a)
(b)
(c)
(d)
(e)
(f)
Simulation results of ZCVS with MAPD: (a) grid voltages, (b) PCC voltages, (c) dc voltage, (d) active current and positive/negative reactive currents, (e) phase currents, (f) active
power.
73
4.4.4 Test Case C: ZCVS Method under Various X/R Ratios
In the previous test cases, the ZCVS was applied to inductive grids (i.e., X/R>>1).
The ZCVS is tested here in two other systems: a resistive grid and a grid with
X/R=1. Fig 4.8 demonstrates the successful results of the ZCVS. As Fig 4.8(a)
reveals, the ZCVS uses only the active current component in positive and negative
sequences in the resistive grid. However, in the grid with X/R=1, both active and
reactive currents in positive and negative sequences have been utilized, as shown
in Fig 4.8(c).
(a)
(b)
(c)
(d)
Simulation results of ZCVS in resistive and X/R=1 grids: (a) injected currents in resistive grid, (b) magnitudes of grid and PCC voltages in resistive case, (c) injected currents in
X/R=1 grid, and (d) magnitudes of grid and PCC voltages in X/R=1 case.
74
(a)
(b)
(c)
(d)
(e)
(f)
Experimental results with traditional and proposed methods, i.e. TVSS (left) and ZCVS (right): (a) grid voltages, (b) magnitudes of grid voltages, (c) obtained reactive currents by TVSS and
ZCVS, (d) phase currents, (e) PCC voltages, and (f) magnitudes of PCC voltages
75
4.5 Experimental Results
To further verify the presented analytical expressions and demonstrate the
performance of the proposed methods, the scaled-down test system is also
employed. The experimental results of the traditional and proposed methods are
obtained under different unbalanced fault conditions and presented in Fig 4.9. Fig
4.9(c) indicate the obtained positive and negative currents by the traditional VSS
and proposed ZCVS. As Figs 4.9(f)-left reveals, traditional method fails to precisely
regulate the phase voltages within the voltage limits. Steady-state over-voltage up
to 1.32 pu and under-voltage down to 0.68 pu occur by the traditional VSS.
However, the proposed method shows successful performance and accurate phase
voltage regulation.
4.6 Conclusion
This chapter proposed an advanced MAS scheme to precisely regulate the phase
voltages of a three-phase GSI within the pre-set safety limits. Conventional
methods mainly suffer from three problems:
1) ignoring the zero-sequence voltage component;
2) neglecting the resistance of the grid impedance; and,
3) zero active power delivery assumption.
The proposed ZCVS method however addressed these three problems.
Moreover, two complementary objectives were also augmented. First, the limited
active power oscillation strategy provided an improved dc voltage while supporting
the ac-side voltage. Second, the corresponding expressions were proposed to
exploit the maximum allowable active power of a distributed energy resource even
under severe unbalances while still regulating the phase voltages. The proposed
voltage support scheme and two complementary strategies bring significant
advantages to emerging DG units. The successful results of the proposed schemes
were verified using simulation and experimental tests.
76
Chapter 5
Parallel MAS Scheme in Multiple
Parallel-Operated Grid-Interactive Smart
Inverters
5.1 Introduction
Parallel operation of converters has been continuously gaining attraction in a wide
range of applications for their modular design, higher scalability, enhanced
reliability, and economical benefits. As their integration increasingly rise, their
contribution in sustaining the host grid stability is strongly demanded. The updating
trend in the grid codes reflects that soon there will be simultaneous requirements
for their LVRT capabilities as well as their effective asymmetrical voltage supports
by advanced active/reactive bi-sequence power provision under unbalanced grid
faults. Addressing these demands in an optimized way becomes very challenging.
This chapter thus proposes a generalized MAS methodology to:
1) coordinate the asymmetrical ride-through and voltage support capabilities
of different parallel-operated GSI units,
2) maximize the utilization of each unit and their collective contribution in
boosting the positive-sequence voltage and reduction of the negative-
77
sequence voltage subject to the constraints from both DG and grid points of
views.
Grid
PCC
B1
Unbalanced fault
Load
A typical POMI structure example: a grid-connected hybrid energy source system with “n” inverters
The simulation tests on ABB 2.0 MVA central inverters illustrate promising
results of the proposed ideas.
5.2 Parallel-Operated Inverters
Continuously rising integration of grid-interactive converter-interfaced power
units, such as DG units, microgrids, and high-voltage direct-current systems, is a
vital part of the power systems evolution towards future smart energy grids. These
fast developments will bring crucial reliability and stability concerns in future
power grids [59]. Extensive studies have been carried out recently to present
different methods for supporting the PCC voltage under unbalanced grid faults by
a single DG unit, shown in Fig 2.1 [44]-[53]. Chapter 3 overviewed these voltage
support strategies, and Chapter 4 introduced an advanced MAS scheme for a single
GSI. Chapter 3 also introduced a combined regulation scheme, named ART
scheme, for simultaneous asymmetrical voltage support and LVRT requirements
78
where different boundary curves are defined, specifically for asymmetric grid
faults. In previous chapters, the ART and MAS schemes were provided for a single
DG unit enforcing its safe operation as well as empowering its maximum grid
supportive capabilities.
However, the coordination of multiple three-phase GSI units for providing
maximum asymmetric grid support, also known as MAS performance, is not
addressed in the literature. This gap ranges from the coordination of MAS
performance for multiple distributed GSI units (e.g., in an active distribution
network or in a microgrid) to effective MAS scheme for the parallel-operated multi-
inverter (POMI) structures.
Most recently, parallel operation of converters has been attracting continuous
attention in different applications, providing the modular converter design
advantages, higher reliability, and economical benefits [93]-[95]. Fig 5.1
demonstrate a typical POMI structure widely utilized in various applications such
as grid-interactive hybrid energy sources [96]-[97], interlinking applications in
hybrid microgrids [98], hybrid multi-microgrid systems [99], multiple parallel-
operated DG units in islanded microgrids [100]-[103] and more.
This chapter proposes an advanced methodology for optimized asymmetric
support performance of a POMI system, named parallel maximum asymmetric
support (PMAS) scheme. The study in this chapter shows that the MAS
performance of each GSI unit inside the POMI structure does not provide the
optimized overall MAS performance. On the other hand, the augmentation of the
multiple GSI units will not provide the optimized overall MAS of the POMI system
neither. These are analytically demonstrated in the following sections. Simply,
neither individual operation nor augmentation will give optimal overall MAS since
in practice multiple GSI units inside the POMI structure will have:
1) different MVA ratings,
2) different safety constraints and fault-tolerance capabilities,
3) more importantly, varied instantaneous operating points.
79
The last factor is a common scenario when hybrid energy sources (for
instance wind and solar) are combined to provide complimentary power generation
(e.g., during the day solar is operating at its full capacity while typically wind is
operating at its high capacity during the night),
Therefore, the smart approach would be to tackle this problem by an advanced
coordination scheme between the GSI units for the optimized overall MAS
performance of the entire POMI structure. The proposed PMAS scheme thus aims
to:
1) coordinate the maximum flexible asymmetrical voltage support and ride-
through capabilities of individual units inside the POMI structure
2) maximize the collective dynamic contribution of POMI system in boosting
the voltage and reducing the imbalance subject to the constraints of the plant
and host system
3) keep the active power injection of each GSI unit intact which leads to
power/cost saving in the plant operation as well as host system stability
enhancement
4) set different objectives based on the potential requirements in future grid
codes
These contributions have been illustrated using the simulation test results.
5.3 System Description
The essential objectives in riding through unbalanced faults and providing grid
supports by the PMAS scheme are 1) avoiding any damage or undesirable operation
in each inverter, and 2) flexibly supporting the asymmetrical voltage (i.e., by
boosting the positive-sequence voltage while alleviating the negative-sequence
component) to the maximum capacity of each inverter. Fig 1(b) illustrates a
schematic of a POMI structure with n inverters. An unbalanced grid fault or loading
can cause asymmetrical voltage condition at the PCC. For any
80
unbalanced condition, the positive- and negative- sequence voltage vectors can be
written in the αβ frame as
,
,
,
,
cos( t ),
sin( t )
cos( t )
sin( t )
k k kk
k k k
k k kk
k k k
v Vv
v V
v Vv
v V
α
β
α
β
ω δ
ω δ
ω δ
ω δ
+ + ++
+ + +
− − −−
− − −
+ = = + + = = − +
(5.1).
The total injected current by kth inverter can be written in its active and
reactive components as
, ,k p k q ki i i= + (5.2).
To exploit a flexible voltage support performance from each unit, the injected
reactive current vector of the kth inverter, iq,k, in (2) is divided into the positive and
negative sequences in (3). These two current components can be written in a vector
form of
, , , ,, , ,
, , , ,
sin ( ) sin ( )
cos ( ) cos ( )
q k q k k q k kq k q k q k
q k q k k q k k
i I t I ti i i
i I t I t
α
β
ω δ ω δ
ω δ ω δ
+ + − −+ −
+ + − −
+ − + = + = = − + − +
(5.3),
where the superscripts “+”/“-” and subscript “q” denote the positive/negative and
reactive component, respectively.
For now, let' s assume that the problem can be solved by the augmentation
method. The augmented amount of the total required reactive currents from all
inverter s for the unbalanced voltage support is augqi .This current can augmented
comprise positive- negative and- .sequencesThe mathematical expression for the augqi can be found by following the augmentation approach and adopting from the
cturesingle DG unit stru ] 52[ , ]92[ , as:
, , , , , , ,1:
( ) ( )q aug q aug q aug q k q k q load q loadk n
i i i i i i i+ − + − + −
== + = + − +∑
, ,,ref g g refq aug q aug
g g
V V V VI I
X X
+ + − −+ −− −
= = (5.4),
81
where n is the number of inverters and ,q loadi is the total reactive currents of the
loads. Then, these currents can be divided among the inverters proportional to their
ratings as:
, , ,
1:
, , ,
1:
. ,
.
kq k k q aug q aug
jj n
kq k k q aug q aug
jj n
SI R I IS
SI R I IS
+ + +
=
− − −
=
= =
= =
∑
∑
(5.5).
It is worth mentioning that for the augmentation approach the instantaneous
operating conditions and the constraints of all inverters should be the same. The
augmented notion can only be applied if the operating conditions of all units are the
same at the fault instant which is not the case for most of the practical applications.
The peak current limitation of the power switches is the main constraint that
must be considered in the PMAS performance. Applying this constraint ensures
flexibly delivering the maximum allowable supportive currents in positive- and
negative- sequences without exceeding the peak current limitation in the kth unit.
The analytical expressions of the phase currents can be formulated in the two-axis
stationary reference frame, based on the unbalanced voltage sag characteristics of
(5.1), i.e., kV + , kV − , kδ+ , and kδ
− as:
, , ,,
, , , ,
cos ( ) sin ( ) sin ( )
sin ( ) cos ( ) cos ( )
p k k q k k q k kkk
k p k k q k k q k k
I t I t I tii
i I t I t I tα
β
ω δ ω δ ω δ
ω δ ω δ ω δ
+ + + + − −
+ + + + − −
+ + + − + = = + − + − + (5.6).
Simplifying (5.6) gives
1, 2,,
, 1, 2,
cos ( )
sin ( )
k kk k
k k k k
I Ii ti I I t
α αα
β β β
ω δ
ω δ
+ + +
+ + +
+ = ⊗ +
(5.7),
where
1, , , 2, , ,
1, , , 2, , ,
sin , cos
sin , cos
k p k q k k k q k q k k
k p k q k k k q k q k k
I I I I I I
I I I I I I
α α
β β
γ γ
γ γ
+ + − + + −
+ + − + + −
= + = −
= − = − −
82
Now, let’s transfer the currents to the three-axis reference frame by the Clarke
transformation as
2 221, 2,a,
2 2 23 31 1b, 1, 1, 2, 2,2 2 2 22 2 23 31 1c, 1, 1, 2, 2,2 2 2 2
( ) ( )
( ) ( )
( ) ( )
k kk
k k k k k
k k k k k
I II
I I I I I
I I I I I
α α
α β α β
α β α β
+ = − + + + − − + −
(5.8).
This gives the magnitude formulations of the current in three phases. Using
(5.6) and (5.8), the following equations can be obtained
( ) ( )2 22lim,a, , , , ,sin cosk p k q k k q k q k kI I I I Iγ γ+ − + −≥ + + − (5.9)
( )( )
22 31lim,b, , , ,2 2 3
23 1
, , ,2 2 3
sin( ) ...
cos( )
k p k q k q k k
p k q k q k k
I I I I
I I I
π
π
γ
γ
+ + −
+ + −
≥ + + +
+ − + − + (5.10)
( )( )
22 31lim,c, , , ,2 2 3
23 1
, , ,2 2 3
sin( ) ...
cos( )
k p k q k q k k
p k q k q k k
I I I I
I I I
π
π
γ
γ
+ + −
+ + −
≥ − + − −
+ + − − (5.11),
where typically
lim,a, lim,b, lim,c, lim,:k k k kI I I I= = = (5.12).
5.4 Plane of Negative Reactive vs. Positive Reactive
(NRPR)
It is proposed in this chapter to use peak-current equations and draw their
dynamic boundaries in the ,q kI − vs ,q kI + plane, as shown Fig 5.2. This plane is called
NRPR in this chapter. Using (5.9)-(5.11), three analytical relations are obtained
between ,q kI − and ,q kI + . Eqs. (5.7)-(5.12) show that the relations between ,q kI − and
,q kI + in the peak-current limitation (PCL) constraints of each unit depend on three
principal parameters:
83
1) the pre-set value of lim,kI (based on the kth unit’s data-sheets),
2) the instantaneous value of the active power component of the current in
that unit, i.e., ,p kI + , which can be a time-varying magnitude based on the
output power of the unit at the duration of support (DOS), and
3) the unbalanced fault characteristics, i.e., kδ+ , and kδ
− . For instance, if the
unbalanced voltage sag occurs in phase A, k kδ δ π+ −− = and three
equations of (5.9)-(5.11) are simplified as
2 2, lim, , ,q k k p k q kI I I I− + +≤ − − (5.13)
2 2 2 2, , , , , , , lim,3q k q k q k q k p k q k p k kI I I I I I I I+ − + − + + ++ − + + ≤ (5.14)
2 2 2 2, , , , , , , lim,3q k q k q k q k p k q k p k kI I I I I I I I+ − + − + − ++ − + + ≤ (5.15)
Eqs. (5.9)-(5.11) are named EQ-Ia, EQ-Ib, and EQ-Ic, represented in Fig 5.2
in blue, orange, and yellow colors, respectively. Based on these equations, the three
curves representing the relationship between ,q kI − and ,q kI + for each of the three
phases are drawn in the NRPR plane, as shown Fig 5.2.
5.4.1 Allowable Current Areas in NRPR Plane
Based on the EQ-Ia, EQ-Ib, and EQ-Ic equations in (5.9)-(5.11), the graph of
Fig 5.2 reveals important information such as the dynamic non-linear and time-
varying relation between the ,q kI − and ,q kI + based on three varying parameters: i)
setting parameters of the converters (i.e., Ilim,k), ii) instantaneous active power
component of the injected currents (i.e., , (t)p kI + ), and iii) unbalanced voltage
characteristics (i.e. kγ ). It is worth mentioning that Fig 5.2 is just an snapshot for
the set parameters of Ilim,k, , (t)p kI + , and kγ . These parameters vary over time
depending on the operating conditions and the fault characteristics.
84
One of the main information extracted from this graph is the allowable current
area at each instant for the flexible combination of the ,q kI − and ,q kI + . The shaded
green area of Fig 5.2 illustrates the snapshot of the allowable current area for the
following conditions: a single-phase to ground fault occurs at phase while Ilim,k is
set to 1.3 p.u. and , (t) 0.2 . .p kI p u+ = at the time of the fault.
A snapshot of the dynamic allowable current area and peak-current boundaries of phases a, b, and c in the NRPR plane for kth inverter at the DOS when a single-phase to ground
fault occurs at phase “A”, i.e., kγ π= ( Test Case A).
5.4.1 Allowable Flexible Voltage Support Areas
The allowable flexible support areas (AFSAs) can be also identified in the NRPR
plane for all units. For instance, Fig 5.3 shows the NRPR plane of similar conditions
to those in Fig 5. 2 with two different values of the instantaneous active power, i.e.,
, (t) 0.4 . .p kI p u+ = and , (t) 0.8 . .p kI p u+ = . As shown in Fig 5.3-(a), higher values of Ip will
decrease the allowable current areas in the NRPR plane. For the purpose of this
chapter, only the positive values of ,q kI − and ,q kI + are important. Fig 5. 3-(b) thus
shows the zoomed view of Fig 5.3-(a) to illustrate only the positive values of ,q kI −
and ,q kI + . This figure also shows two AFSAs for two values of the instantaneous
active power. Light green and dark green areas show the AFSAs for , (t) 0.4 . .p kI p u+ =
85
and , (t) 0.8 . .p kI p u+ = , respectively. As it is clear from Fig 5.3-(b) that higher
instantaneous active power value shrink the AFSA area of the kth unit at the DOS
resulting in lower allowable room for contribution in supporting the unbalanced
voltage by positive- and negative-sequence reactive currents.
(a)
(b)
Two more snapshots of the NRPR plane for a similar inverter at Test Case A when the instantaneous active power has been increase to , (t) 0.4 . .p kI p u+ = and , (t) 0.8 . .p kI p u+ = (b) zoomed
view for the flexible voltage support area.
86
Therefore, based on the instantaneous active current value at the DOS, the
allowable voltage support area of the kth inverter may be varied resulting in very
different optimal reference values for the kth unit as well as for the entire POMI
structure. These plots also show the nonlinear relation between the active current
component value and the AFSA resulting in a complex optimization problem.
5.5 Proposed Optimized Asymmetric Support by PMAS
To find the optimal coordination between inverters inside the POMI structure, the
instantaneous available capacity or AFSA characteristic of each unit should be
considered. The instantaneous available current capacity of each converter during
the DOS depends on the instantaneous active power injection by each unit in
addition to its pre-set values (e.g., rating and maximum peak-current). All these
parameters can be varied for different units at the DOS. A common example is the
case of a hybrid energy source with complementary power generation units, e.g.,
wind and solar as shown in Fig 5.1. Typically, one of the units will have limited
current capacity at the DOS since it is injecting a considerable amount of active
power while other units still have extra capacities available for the flexible
asymmetric voltage support since they are operating in lower active power
operating points. This can provide a useful opportunity for cooperation in the
PMAS optimal supportive scheme. For instance, the active power production of the
solar energy system is in its high during the day while wind typically produces its
high active power at night. Therefore, a smart coordination scheme would benefit
from the optimum available capacity of each unit during the DOS.
Fig 5.4 illustrates the flowchart of the proposed PMAS method. As indicated,
it comprises four stages. In the following sections, these four stages are discussed.
5.5.1 Stage I: Obtaining NRPR Equations
In this section, the current boundaries of all inverters based on the fault
characteristic and their individual instantaneous active power values at the DOS are
obtained using (5.9)-(5.11). As an example, Fig 5.5 indicates a case (Test Case B)
87
where there is 2-DG POMI structure with different settings and operating
conditions. In this test case, DG1 and DG2 are rated at 40% and 60% of the total
MVA of the POMI structure, respectively. Their peak-current values are set to 1.3
and 1.7 in p.u. of their own ratings (i.e., 0.52 and 1.02 in p.u. of total POMI rating).
In addition, they have different amount of active power injection at the DOS. Based
on these different parameters, a single-phase fault on phase “B” will result in totally
different NRPR curves as illustrated in Fig 5.5-(a) and Fig 5.5-(b).
Peak Current Boundaries in RCPN Plane for All CIUs
Extracting AFSA Boundary CurveFor All CIUs
Normalizing Boundary Curves of each CIU to their corresponding
ratings based on POCI total rating
Segmentation of Boundary Curves into finite number of points
Convolution of Boundary Curves
Determining Optimal Values Based on MP,
MN, and MPN
Stage II
Stage I
Stage III
Stage IV
INPUT: Fault Angle, Inst. Active Power of
each CIU
Flowchart of the proposed optimal asymmetric support by PMAS method.
5.5.1 Stage II: AFSA Boundary Curves
In this stage, three boundary curves will be transformed into one curve, named
AFSA curve. First, the positive reactive current of the kth inverter is defined as a
vector:
88
2 2lim, , 2 2
, , lim, ,0 : :k k p kq k AFSA k k p k
R I Ii R I I
M+ −
= − (5.16),
where “M” is the number of segments in the AFSA curves, and , ,q k mI + is the mth
element of the , ,q k AFSAI + vector. Also using “Rk” parameter, , ,q k AFSAI + vector becomes
a normalized vector of ,q kI + in per unit of the total MVA of the POMI system.
Second, the following equations give the negative reactive current AFSA
vector of each inverter:
, ,m 1, , 2, , 3, ,.min( , , )q k k k m k m k mI R y y y− = (5.17),
where , ,mq kI − is the mth element of the , ,q k AFSAi− vector, and
21, , 1, , 1, ,
1, ,4
2k m k m k m
k mB B C
y− + −
= (5.18),
22, , 2, , 1, ,
2, ,4
2k m k m k m
k mB B C
y− + −
=
23, , 3, , 1, ,
3, ,4
2k m k m k m
k mB B C
y− + −
=
where
( )1, , , , ,2 sin cosk m p k k q k m kB I Iγ γ+ += −
( ) ( )2, , , , ,3 cos sin cos 3 sink m p k k k q k m k kB I Iγ γ γ γ+ += × − + × +
( ) ( )3, , , , ,3 cos sin cos 3 sink m p k k k q k m k kB I Iγ γ γ γ+ += × − − + × −
2 2 21, , , lim, , ,k m p k k q k mC I I I+ += − + (5.19).
Fig 5.5-c and Fig 5.6-c demonstrate the results of applying the analytical
methods of Stage II in two test cases.
89
(a) (b)
(c) (d)
(e) (f)
Test Case B: Single-phase fault on phase “B” and DG1 and DG2 are rated at 40% and 60% of the total MVA of the POMI structure, respectively: (a) NRPR curves for DG1, (b) NRPR curves for DG2, (c) Stage II: AFSA boundary curves for DG1 and DG2, (d) Stage III:
convoluted AFSA boundary curves, (e) Stage IV: optimal values of the MTP and MTN strategies, (f) Stage IV: optimal value of the MTPN strategy
90
5.5.2 Stage III: Convolution of Boundary Curves
After identifying the constraints and allowable support areas in Stage I and reducing
the constraints into two smaller and normalized vectors in Stage II, this section
simply convolutes AFSA vectors of all inverters into vectors of vectors or a m*m
matrix for the entire POMI system as:
, ,1 , 1,1 , ,0 , 1,
, , , 1,1 , , , 1,
.. ..
: .. .. :: .. .. :
.. ..
q k q k q k q k M
M M
q k M q k q k M q k M
I I I I
Q
I I I I
+ + + ++ +
+×
+ + + ++ +
+ +
= + +
(5.20)
, ,1 , 1,1 , ,0 , 1,
, , , 1,1 , , , 1,
.. ..
: .. .. :: .. .. :
.. ..
q k q k q k q k M
M M
q k M q k q k M q k M
I I I I
Q
I I I I
− − − −+ +
−×
− − − −+ +
+ +
= + +
(5.21).
Fig 5.5-(d) and Fig 5.6-(d) reveal the results of applying these matrix
convolutions in two test cases where each curve represents the corresponding two
vectors in each column of M MQ+× and M MQ−
× matrices. From these two figures, it is
obvious that the applied numer of segmentation in Stage II was M=6. The 2D
matrices in Eq (5.20) and (5.21) can be generalized to n-D matrices of ...M Mn
Q+−× ×
where n is the number of parallel DG units.
5.5.3 Stage IV: Determination of the Optimal Values
This section is the final section and it explores the ways to find the optimal reference
values for ,q kI − and ,q kI + . Having the M MQ+× and M MQ−
× matrices, many applicable
objectives can be defined to determine the ,q kI − and ,q kI + of all inverters to provide
the global optimality in the POMI system. In this chapter, three simple objectives
are defined as examples.
91
(a) (b)
(c) (d)
(e) (f)
Test Case C: Arbitrary asymmetrical fault with 5 /12γ π= and DG1 and DG2 are rated at 70% and 30% of the total MVA of the POMI structure, respectively: (a) NRPR curves
for DG1, (b) NRPR curves for DG2, (c) Stage II: AFSA boundary curves for DG1 and DG2, (d) Stage III: convoluted AFSA boundary curves, (e) Stage IV: optimal values of the MTP and
MTN strategies, (f) Stage IV: optimal value of the MTPN strategy
92
First, the maximum total positive-sequence (MTP) strategy finds the optimal
values of the ,q kI − and ,q kI + for all inverters where the total positive-sequence
reactive current injection of the POMI system is maximized. This can be easily
determined by finding the maximum value of the M MQ+× matrix. Since the building
vectors of the M MQ+× matrix, i.e., , ,q k AFSAi+ vectors of all units, are ascending the entire
matrix is ascending and the highest point is where
2 2, , lim, ,q k M k k p kI R I I+ = − for all k=1:n (5.22).
This is also clear from ,q totalI + surface in Fig 5.5-(e) and Fig 5.6-(e).
Another approach can be the optimal points to maximize the total negative-
sequence (MTN) reactive current of the POMI system. This means the highest point
in the M MQ−× matrix. This can be also seen in Fig 5.5-(e) and Fig 5.6-(e) where the
following sets for the values of the ,q kI − and ,q kI + of the DG1 and DG2 are obtained.
Test Case B:
,1,1 ,2,2 ,1,1 ,2,20 0.18 . . 0.45 . . 0.61 . .q q q qI I p u I p u I p u+ + − −= = = = (5.23).
Test Case C:
,1,2 ,2,2
,1,2 ,2,2
0.153 0.072 . .
0.507 . . 0.186 . .
q q
q q
I I p u
I p u I p u
+ +
− −
= =
= = (5.24).
As a third and better approach we can define our objective to maximize the
following statement:
M M M M M MQ Q Qα α+− + + − −× × ×= + (5.25),
to combine both positive and negative-sequence reactive currents and provide
optimal flexible asymmetric voltage support. The result of applying this function is
shown in Fig 5.5-(f) and Fig 5.6-(f) where 1α α+ −= = .
93
ABB PVS980 Central Inverter Model [104] block diagram interfacing two renewable DG units, i.e., 2MVA wind and 3MVA solar, to 20MVA grid
(a)
(b)
(c)
94
Test Case D: Conventional voltage support method [43]-[45] (a) grid voltage, (b) PCC voltage, (c) positive- and negative sequence voltages of the grid and PCC.
(a)
(b)
(c)
Test Case D: Conventional voltage support method [43]-[45]: (a) active and positive/negative-sequence reactive currents of DG1, DG2 (b) phase-currents of DG1, DG2, (c)
active and reactive powers of DG1 and DG2.
5.6 Simulation Results
The proposed methods are examined on a simulated version of a practical test
system, adapted from a typical ABB ABB PVS980 Central Inverter [104], as shown
in Fig 5.7. This POMI structure is connected to the medium-voltage distribution
system in Ontario, Canada. The details of this distribution system are provided in
Chapter 6. The system parameters are reported in Fig 5.7. The POMI system
interfaces a 2MVA wind farm and a 3 MVA solar farm to a 27 kV distribution grid.
Each DG has its own integrated energy storage system to balance its dc-link
voltage.
95
Fig 5.8 shows the result of applying the conventional voltage support method
[43]-[45] with constant reactive current injection under the unbalanced fault. This
method has three drawbacks:
1) It is not a maximum unbalanced voltage support.
2) The active power in DG1 (see Fig 5.9-a-left and Fig 5.9-c-left) is
disrupted.
3) There is no coordination between 2 DGs support. There is neither
adjustability in the support process since it is just a constant reactive
power injection based on the unbalanced voltage.
(a)
(b)
(c)
Test Case D: Proposed PMAS voltage support method (a) grid voltage, (b) PCC voltage, (c) positive- and negative sequence voltages of the grid and PCC.
96
(a)
(b)
(c)
Test Case D: Proposed PMAS voltage support method: (a) active and positive/negative-sequence reactive currents of DG1, DG2 (b) phase-currents of DG1, DG2, (c)
active and reactive powers of DG1 and DG2.
On the other hand, the proposed PMAS method addresses these
insufficiencies as illustrated in Fig 5.10 and 5.11.
1) Fig 5.10 shows better positive voltage boost and more negative voltage
reduction.
2) Furthermore, Fig 5.11 reveals the smart coordination between the two
DGs. It is clear from Fig 5.11 that DG2 injects more supportive reactive
currents in the positive and negative sequences since its active power
injection at the DOS is relatively smaller than DG1 (see Fig 5.11-a).
3) Fig 5.11-a and Fig 5.11-c also show that despite higher asymmetric
support by the PMAS compared to the conventional method, the proposed
97
method does not disrupt the active power injection of DG1 due to its
coordination mechanism.
5.7 Conclusion
This chapter proposed an advanced methodology for optimized asymmetric support
performance of a parallel-operated multi-inverter system, named the PMAS
scheme. The study in this chapter shows that the maximum asymmetric support
performance of each inverter unit inside the parallel structure does not provide the
overall optimized performance. On the other hand, the augmentation of the multiple
inverters will neither provide the optimized overall maximum asymmetric support
for the parallel system. This is due to the differences on the inverters different MVA
ratings, different safety constraints and fault-tolerance capabilities, and more
importantly, varied instantaneous operating points. Therefore, the smart approach
would be to tackle this problem by an advanced coordination scheme between the
inverter units for the overall optimized asymmetric support performance. The
proposed PMAS scheme thus empower the parallel multi-inverter system to:
1) coordinate the maximum flexible asymmetrical voltage support and ride-
through capabilities of individual units inside the POMI structure,
2) maximize the collective dynamic contribution of POMI system in boosting
the voltage and reducing the imbalance subject to the constraints of the plant
and host system,
3) keep the active power injection of each GSI unit intact which leads to
power/cost saving in the plant operation as well as host system stability
enhancement, and
4) set different objectives based on the potential requirements in future grid
codes
The simulation tests on ABB 2MVA central inverters illustrated effectiveness
of the proposed ideas.
98
Chapter 6
Decentralized MAS Scheme in Multiple
Distributed Grid-Interactive Smart
Inverters
6.1 Introduction
The active power injection of DG units before and during the fault occurrence is an
important factor affecting the maximum amount of allowable voltage support by
individual DG units. Therefore, to allocate the supportive currents from each DG,
the instantaneous capacity of each DG (i.e., instantaneous available capacity under
the fault) plays a crucial role. The autonomy of the coordination scheme can also
be highly beneficial since it eliminates (or at least reduces) the reliance on
communication systems, central data acquisition/processing, and supervisory
control. This leads to saving the costs while increasing the reliability of the highly-
integrated active distribution networks (ADNs). However, coordinating the
asymmetrical voltage support among multiple DG units while maximizing their
contribution is very challenging for the autonomous/decentralized methods since
there exists many constraints but no communication between the units.
99
The main achievement of this chapter is to propose an autonomous
cooperative scheme to address these objectives. The main contributions of this
chapter are the followings:
1) A comprehensive decentralized asymmetrical ride-through scheme is
proposed in this chapter. The objective is coordinating the flexible
asymmetrical voltage support contribution of multiple converter-interfaced
DG units in an ADN such that their supports neither interfere with each other
nor worsen the faulty situation. There is no need for the central control unit
in the proposed coordination scheme, avoiding the high costs of
communication infrastructures and increasing the reliability and flexibility
of the ADN and DG units.
2) The active power injection of DG units is not affected during the support
time; saving power and cost (important from the DG owner point of view)
and improving the host system stability (important from the system operator
point of view). This is achieved by considering both instantaneous active
power injection and active power oscillation limit of individual DG units
during the support in the proposed strategies.
3) The maximum flexible asymmetric voltage support performance is not
compromised whenever one DG reaches its limits since other DG units can
instantaneously compensate for that due to the cooperative nature of the
proposed method. In addition, the over-voltage problem on the un-faulted
phases are considered in the coordination scheme.
A new concept is proposed to build a comprehensive coordination scheme,
named maximum support point tracking. This technique is achieved using the
identified boundary limits and dynamic support points trajectories.
100
(a)
(b)
Active distribution network with (a) single and (b) multiple DG units.
6.2 Multi-DG Active Distribution Network
A single DG unit connected to the grid under the unbalanced condition is indicated
in Fig 6.1(a). Extensive studies have been carried out recently to present different
methods for supporting the PCC voltage under unbalanced grid faults by a single
DG unit [36]-[53].
On the other hand, a multi-DG system under unbalanced grid faults,
illustrated in Fig 6.1(b), has not been thoroughly investigated in the literature. The
101
voltage control techniques in active distribution networks (ADNs) proposed in the
existing literature are commonly classified as centralized and decentralized
methods. An in-depth literature review of these two categories is presented in [105]-
[107]. The centralized voltage control methods typically use communication signals
for controlling distributed loads, multiple DG units, and distributed storage
systems. Such an active centralized scheme results in the accumulation of the
information and requires signal processing and decision-making units as well as
communication infrastructures to transmit all the signals [108]. Although the
centralized methods can lead to optimal management of the ADNs and economic
dispatch of DG units with high accuracy and controllability, in theory, they suffer
from several important drawbacks in practice:
1) computation complexity in gathering and processing the information and
optimal decision making;
2) challenges of optimal decision making based on the limited information,
e.g., when the information of one area is not available;
3) defected operation in the entire network in the case of a failure in one
control unit;
4) high costs of building communication infrastructures; and (5) undesirable
impact on the plug-and-play feature of the distributed units [105]-[106].
Therefore, some efforts have been carried out in the recent literature to
propose proper decentralized voltage control methods in microgrids [106]-[107],
[109]-[114] and ADNs [105], [115] as well as distributed consensus-based control
strategies in smart grids [116]-[117]. However, none of these studies has considered
asymmetrical voltage support and LVRT performance improvement in ADNs with
multiple DG units.
102
6.3 Proposed Decentralized Maximum Flexible
Asymmetrical Support Tracking Scheme
The essential objectives in riding through unbalanced faults and providing grid
supports by a single DG unit are to avoid any damage or undesirable operation in
the DG unit, and flexibly support the asymmetrical voltage (i.e., by boosting the
positive-sequence voltage while alleviating the negative-sequence component). Fig
6.1(b) illustrates a schematic of an ADN with n converter-interfaced DG units. An
unbalanced grid fault or loading can cause asymmetrical voltage condition in the
entire distribution network. For any unbalanced condition, the positive- and
negative- sequence voltage vectors can be written for each unit (similar to the
unbalanced voltage equations for the POMI system in the previous chapter) as
, ,
, ,
cos( t ) cos( t ),
sin( t ) sin( t )k kk k k k
k kk kk k k k
v vV Vv v
v vV Vα α
β β
ω δ ω δ
ω δ ω δ
+ −+ + − −+ −
+ −+ + − −
+ + = = = = + − +
(6.1).
The total injected current by kth DG unit can be mathematically formulated
as , ,k p k q ki i i= + (6.2).
To exploit a flexible voltage support performance from distributed units, the
injected reactive current vector of the kth converter, iq,k, in (6.2) is divided into the
positive and negative sequences in (6.3). These two current components can be
written in a vector form of
, , , ,, , ,
, , , ,
sin ( ) sin ( )
cos ( ) cos ( )
q k q k k q k kq k q k q k
q k q k k q k k
i I t I ti i i
i I t I t
α
β
ω δ ω δ
ω δ ω δ
+ + − −+ −
+ + − −
+ − + = + = = − + − +
(6.3).
For now, let' s assume that the augmented amount of the total required
reactive currents from all distributed units, augqi ,for the unbalanced voltage support
is available. This augmented current can comprise positive - and negative-
sequences and can be found by following the notions for the single DG unit
structure ] 51[- ]52 .[ It is worth mentioning that for conventional augmented
approaches the operating conditions of distributed units should be assumed to be
the same.
103
Control system diagram of the proposed DMAS scheme embracing the DSPM and MSPT blocks
After determining the total required positive- and negative-sequence currents
by the augmented notion, the problem becomes dividing the total supportive
currents between the distributed converters. The Kirchhoff’s current law gives
, ,1:
aug totalq q k q load
k ni i i
== −∑ (6.4),
where n is the number of distributed units and ,totalq loadi is the total reactive currents of
the loads. The positive and negative-sequence can then be divided based on the
ratings of the distributed units by drop-based approaches.
For an effective distributed voltage support, the nearest converter (i.e., with
the lowest line impedance) can contribute more to support the voltage, if all the
converters have the same amount of the available capacity for additional reactive
104
current injection. Therefore, the default distributed assignment of the set-points can
be realized using the following equation:
1 1
, ,g , ,g1 1
1: 1:
,k k
j j
X Xq k q q k q
X Xj n j n
I I I I+ + − −
= =
= =∑ ∑
(6.5),
where Xi is the inductance of the line connecting the ith converter to the PCC. The
ratings of the DG units and their corresponding peak currents during the
asymmetrical condition must also be considered prior to the augmentation.
However, this augmented notion can only be applied if the operating conditions of
all distributed units are the same at the fault instant, or there exists a central control
unit. Hereinafter, the time interval in which the proposed voltage support method
is applied is called the duration of support (DOS).
To find the decentralized coordination between individually optimized
flexible asymmetric voltage supports of multi-DG structure in Fig 6.1(b), the
following points should also be considered in addition to the rating and maximum
peak current of each unit:
1) Available capacity of each converter during the DOS: There might be a case
that one unit reaches its maximum current capacity at the DOS since it is
injecting a considerable amount of active power while other units still have
extra capacities available for the support (since they are operating in lower
active power operating points). This is a common scenario in ADNs with
both solar and wind energy units which can create a useful opportunity for
cooperation. During the day, the active power production of the solar energy
system is typically in its high while during the night wind produces its high
active power. Therefore, a smart coordination scheme would benefit from
the optimum available capacity of each unit during the DOS.
2) Active power oscillation of each converter during the DOS: This parameter
should be kept under control for a stable operation and reliable distributed
support. High active power oscillation (due to the severe unbalanced faults)
105
harms the frequency stability of the ac-side as well as dc-side voltage
stability.
3) Un-faulted phase voltage magnitudes: The over-voltage on the un-faulted
phases must be avoided. This can be achieved by the dynamic nature of the
proposed method.
4) Maximum utilization of the kth unit in a dynamic and autonomous manner.
The proposed coordination scheme is named decentralized maximum
asymmetrical support tracking (DMAS) which encompasses two core blocks:
1) dynamic support point movement (DSPM), and
2) maximum support point tracking (MSPT).
Fig 6.2 illustrates the control system of the proposed DMAS scheme with its
DSPM and MSPT blocks. These control blocks are explained in the following
sections.
6.4 Identified Constraints for MSPT Method
This section explains how to find the maximum allowable support of kth DG
unit. The MSPT method defines two criteria: maximum tolerable active power
oscillation limit (POL) and peak current limit (PCL). Then, the appropriate
reference values for the positive- and negative-sequence reactive currents will be
determined.
106
Proposed MSPT approach with FRPN strategy
6.4.1 Active Power Oscillation Limit (POL) Constraint
Based on the instantaneous power theory, the output active power oscillation
terms of the kth DG unit is calculated as
. .k k k kp v i v i+ − − += + (6.6).
The maximum active power oscillation of the kth unit can be formulated as
2 2max,k , , ,( ) ( )k q k k q k k p kp V I V I V I+ − − + − += − + (6.7).
Therefore, depending on the instantaneous amount of pI + in the kth unit, the
following relation between the ,q kI − and ,q kI + is obtained:
( )22lim,k , ,
,k p k k q k
q kk
P V I V II
V
− + − +−
+
− +≤
(6.8).
This is the first obtained constrain between ,q kI − and ,q kI + . Eq (8) is named EQ-
POL for representing the POL constrains the MSPT graphs. The EQ-POL boundary
107
is sketched as a straight line in Fig 6.3 in magenta color. This analytical equation
does not allow the active power oscillation of kth unit exceeds its corresponding
limitation, lim,kP . The value of lim,kP is set by the converter’s manufacturer or owner.
This feature thus avoids any undesired damage to the converter and the control
system of the kth unit. Furthermore, it enhances the ac-side frequency stability and
dc-side voltage stability during severe unbalanced grid faults.
(a)
(b)
Allowable flexible voltage support areas of (a) mth DG unit with four different values of Ip,m at the DOS, and (b) lth DG unit with four different values of Plim,l at the DOS
108
It is worth mentioning that the EQ-POL boundary may be time varying during
the DOS featuring the dynamic characteristic of the proposed MSPT since (8)
indicates that the relation between ,q kI − and ,q kI + in the POL constraint of the kth unit
depends on:
1) the instantaneous value of the active power component of the current in
that unit, i.e., ,p kI + , during the DOS, and
2) the unbalanced fault characteristics, i.e., kV + and kV − .
6.4.2 Peak-Current Limitation (PCL) Constraint
The peak current limitation of the power switches is another important constraint
that must be considered in the MSPT method. Applying this constraint ensures i)
flexibly delivering the maximum allowable supportive currents in positive- and
negative- sequences and ii) autonomously setting the reference values of ,q kI − and
,q kI + without exceeding the peak current limitation in the kth unit. The analytical
expressions of the phase currents can be formulated in the two-axis stationary
reference frame, based on the unbalanced voltage sag characteristics. Similar
analysis to the parallel system in the previous chapter can also be carried out here.
Eq (5.9)-(5.11) can be also used here for the peak current limitation constrains in
distributed GSI units. These equations are respectively named EQ-PCL-a, EQ-
PCL-b, and EQ-PCL-c, represented in Fig 6.3 in blue, orange, and yellow colors,
respectively. Based on these three equations the graph of Fig 6.3 becomes complete.
These three equations besides the EQ-POL determine the non-linear and time-
varying constraint boundaries for ,q kI − and ,q kI + . In summary, these boundaries
depend on three factors: i) setting parameters of the converters (i.e., Ilim,ks and
plim,ks), ii) unbalanced voltage characteristics, and iii) instantaneous active power
component of the injected currents. Based on these three factors, the four curves
representing the relationship between ,q kI − and ,q kI + are drawn in Fig 6.3 to better
illustrate the proposed MSPT approach.
109
6.4.3 Allowable Flexible Voltage Support Areas
Based on the proposed ideas in this chapter, the allowable flexible support areas
(AFSAs) can be identified in the NRPR plane for all units. As a first example, the
AFSA of the kth DG unit is shown with the green area in Fig 6.4 considering its pre-
set configurations as well as instantaneous operating points at the DOS. The green
areas of Fig 6.4 show other examples of AFSAs. Fig 6.4(a) illustrates four different
AFSAs (from light green to dark green) for four different values of the active
current of the mth DG unit at the DOS. Therefore, based on the instantaneous active
current value at the DOS, the allowable voltage support area of the mth DG unit may
be varied resulting in very different optimal reference values for the positive- and
negative-sequence reactive currents of that specific unit. It is clear from Fig 6.4(a)
that higher active current values of the DG unit at the DOS results in lower
allowable room for contribution in supporting the unbalanced voltage by positive-
and negative-sequence reactive currents. These plots clearly show the nonlinear
relation between the active current component value and the permissible values for
the supportive reactive currents in positive- and negative sequences.
Fig 6.4(b) also demonstrates four different AFSAs (from light green to dark
green) for another DG unit based on four different values of the maximum tolerable
active power oscillation. Based on Fig 6.4(b), if the maximum tolerable active
power oscillation amount of the lth DG unit decreases, the available area of its
flexible voltage support contribution will shrink. Therefore, other DG units shall
compensate for the shrunk area of support in the lth DG unit in the collaborative
MSPT approach within their own available green areas. The introduced AFSAs
give useful insights on how to drive appropriate strategies in a decentralized manner
to achieve coordinated flexible support by multiple distributed units.
110
PCL equations for the entire range of possible asymmetrical fault types, i.e.,
0 : : 212kπγ π= for two different cases.
6.4.1 Simplified MSPT
We can also use a simplified version of the MSPT approach in the control system
(i.e., MSPT block of Fig 6.2) to reduce the computational complexity. Fig 6.5
demonstrates all possible EQ-PCLs for any type of asymmetrical faults. Fig 6.5
reveals an interesting feature in the NRPR plane: for any type of asymmetrical faults
we can find two useful points (i.e., full positive support point, Pfps, and full negative
111
support point, Pfns) such that a line connecting these two points gives a good
estimation of the all possible EQ-PCLs boundaries. This simplification approach
effectively removes the dependency of the PCL equations (5.9)-(5.11) to the
asymmetrical fault type. Manipulating (5.9)-(5.11) gives
2 2, , , lim, ,
, , , lim, ,
: 0,
: 0,
fps q k q k fps k p k
fns q k q k fns k p k
P I I I I
P I I I I
− +
+ −
= = −
= = − (6.9).
Using this simple approach enormously expedites the calculation and can be
very efficient in the case of real applications with low-speed processing units.
Maximum support point tracking with BAMP
6.5 Proposed Strategies to Determine Maximum Support
Points by DSPM
Now that we have identified the constraints and allowable support areas, the final
stage of the MSPT approach is to find the optimal reference values for ,q kI + and ,q kI −
in an autonomous way for individual units. The following subsections introduce
112
two strategies to track and find the optimal values for ,q kI + and ,q kI − without any
communication between the distributed units.
6.5.1 MSPT with Flexible Ratio between Positive- and Negative-
Sequences (FRPN)
The relation between the desired ,q kI − and ,q kI + values can be defined by:
, ,,
, ,
q k g ref k kFRPN k
q k ref k g k
I V V V MI V V V
− − − −
+ + + +
− ∆= = =
− ∆ (6.10).
This equation governs the ratio between the desired positive and negative
voltage supports, i.e., MFRPN, and it is named EQ-FRPN. The EQ-FRPN is the line
sketched in green color in Fig 6.3. The maximum support points are thus
determined by the intersection of EQ-FRPN line and one of the boundary curves,
i.e., EQ-POL, EQ-PCL-a, EQ-PCL-b, and EQ-PCL-c. For example, points P1 and
P2 in Fig 6.3 indicate the peak-current limitation of phase B and the maximum
values for the positive- and negative-sequence reactive currents respectively for
0.15FRPNM = and 0.3FRPNM = . Point P3 shows the peak-current limitation of phase
A and the maximum values for the positive- and negative-sequence reactive
currents for 0.6FRPNM = . The slope of the EQ-FRPN line can vary flexibly during
the DOS to reach the equilibrium point between the distributed units in an
autonomous way.
6.5.2 MSPT with Bounded Autonomous Moving Points (BAMP)
Approach
As opposed to the FRPN strategy, the MSPT with the bounded autonomous moving
points (BAMP) does not require a ratio between ,q kI + and ,q kI − . Instead, it suggests
defining one initial support point (Pisp) and one final support point (Pfsp). The
corresponding ,q kI + and ,q kI − for the initial and final points can be obtained by
113
1 1
, , , ,1 1
1: 1:
1 1
, , , ,1 1
1: 1:
,
,
k k
j j
k k
j j
X Xisp ispq k isp q k isp
g gX Xj n j n
X Xfsp fspq k fsp q k fsp
g gX Xj n j n
V VI I
X X
V VI I
X X
+ −+ −
= =
+ −+ −
= =
∆ ∆= × = ×
∆ ∆= × = ×
∑ ∑
∑ ∑
(6.11).
These expressions are named EQ-BAMP and depicted in Fig 6.6. According
to Fig 6.6, the voltage support area for this case (i.e., without constraints) includes
both green and gray areas. However, if the MSPT constraints are applied, then the
moving points will be limited to just the green area. Two very useful features can
be extracted from Fig 6.6.
1) Generally, if the positive-sequence reactive current increases during the
dynamic voltage support (e.g., starting from point Pisp), it is most likely to
hit the PCL constraint boundaries.
2) Generally, if the negative-sequence reactive current increases during the
bounded moving points strategy, it is most likely to hit the POL constraint.
Based on these useful features obtained from the NRPR plane, we can
properly design our MSPT approach with BAMP strategy (see Fig 6.2). It is thus
proposed in this chapter that the MSPT with POL constraint is applied to adjust the
negative-sequence reactive current while the equations of the PCL constraints are
considered for regulating the positive-sequence reactive current. The simulation
results will better clarify the proposed concepts
114
Studied Test System: A typical medium-voltage distribution system in Ontario, Canada
6.6 Simulation Results
The proposed methods are examined on a practical test system, adapted from a
typical Hydro One system, the medium-voltage distribution system in Ontario,
Canada [118]. The system parameters are reported in Fig 6.7. This 27-kV
distribution network consists of three large renewable plants (2MVA wind farm,
2.5 MVA solar farm, and 3MVA hybrid plant). As Fig 6.7 also indicates, the pre-
set PCL/POL values of three DGs are different (Ipeak,1=1.5 p.u., Ipeak,2=1.2 p.u.,
Ipeak,3=1.8 p.u., Plim,1=0.5 p.u., Plim,2=0.5 p.u., and Plim,3=0.7 p.u.,).
6.6.1 Test Case A: Conventional vs Proposed
A double-phase fault occurs at t=0.1s and clears at t=0.4s, as shown in Figs 6.8 and
6.10. Fig 6.8 and 6.9 show the results of the conventional asymmetrical voltage
support method [44], [83], [91]. In the conventional approach, all three DGs inject
similar amount of positive- and negative- sequence currents, respectively,
115
proportional to the positive-sequence voltage reduction (from a specific value, e.g.,
0.9 p.u. [44]) and negative-sequence voltage rise (from a specific value, e.g., 0.05
p.u. [44]). Although there are huge differences between the instantaneous
supportive capacity of each DG (in addition to differences between their pre-set
values, i.e., ratings and PCL/POL constraints), they inject both sequences with
respect to two simple droop control techniques. Due to the simplicity of the
conventional method, some grid codes have adopted it [83]. However, the results
obtained from the conventional approaches are neither sufficient nor coordinated.
This is clear by comparing Fig 6.8(b)-(c) with Fig 6.10(b)-(c).
(a)
(b)
(c)
Test Case A: Conventional voltage support method [44], [83], [91] (a) grid voltage, (b) PCC voltage, (c) positive- and negative sequence voltages of the grid and PCC.
116
(a) (b)
Test Case A: Conventional voltage support method [44], [83], [91]: (a) active and positive/negative-sequence reactive currents of DG1, DG2, and DG3, (b) phase-currents of
DG1, DG2, and DG3
On the other hand, Figs 6.10 and 6.11 illustrate the results of the proposed
scheme. The active current components of DG1 and DG2 are high during the DOS.
Event-1: According to Fig 6.11(b), in the first milliseconds after the fault
occurrence, the peak-current in phase A in DG2 hits the limitation. Therefore, the
proposed MSPT method tries to autonomously and dynamically adjust the positive-
sequence reactive current of the DG2 (see Fig 6.11(a), event-2) so that the peak-
current limitation criterion is satisfied while still contributing to the distributed
voltage support (to the maximum capability of DG2). Event-3: To compensate for
this shortage, DG1 autonomously tries to inject more positive-sequence reactive
current as it is clear from t=0.2s to t=0.32s in Fig 6.11(a). Event-4: At this point,
DG1 also hits the peak-current limitation in phases A and B, as shown in Fig
6.11(b). Therefore, the proposed MSPT method autonomously keeps its positive-
117
sequence reactive current constant, as indicated in Fig 6.11(a), event-5. Event-6:
From this point, DG3 autonomously tries to inject even more positive-sequence
reactive current, as accelerated increase is observable in Fig 6.11(a), to compensate
for the shortcomings of positive-sequence support in DG1 and DG2.
Comparing Fig 6.8(b)-(c) with Fig 6.10(b)-(c) clearly illustrates the superior
performance of the proposed DMAS scheme in supporting the phase voltages as
well as in improving positive- and negative-sequences of the voltage.
(a)
(b)
(c)
Test Case A: the proposed DMAS scheme, (a) grid phase-voltages, (b) PCC phase-voltages, (c) positive- and negative- sequence voltages of the grid and PCC.
118
(a) (b)
Test Case A: the proposed DMAS scheme: (a) active and positive/negative-sequence reactive currents of DG1, DG2, and DG3, (b) phase-currents of DG1, DG2, and DG3
6.6.2 Test Case B: Proposed Scheme under Severe Conditions
In this test case, two different voltage drops 100% on phases A and 50% on phase
B (as shown in Fig 6.12(a)) have been applied to test the proposed coordination
scheme. The result of the DMAS voltage support is presented in Fig 6.12(b). Fig
6.12(c) also illustrates the improvements in positive- and negative-sequence
voltages. During the dynamic and autonomous operation of the proposed DMAS
method in this test case, five noticeable MSPT events happen (i.e., first in DG2,
then in DG1, and finally in DG3). Event-1: At t=0.15s, the peak-current limitation
of DG2 (Fig 6.13(b)) causes to reduce the positive-sequence reactive current (Fig
6.13(a), event-2). This event is autonomously compensated by accelerated increase
in positive support contributions from DG1 and DG3 from t=0.15s, event-3. Event-
4: Another main MSPT event occurs at 0.22s in DG1 due to peak-current limitation.
Event-6: A few milliseconds later, another MSPT constraint occurs at t=0.32s
119
where the active power oscillation of the DG1 hits the pre-set maximum allowable
limit (Fig 6.13(b)). Therefore, the DMAS immediately reduces the negative-
sequence reactive current in DG1 (Fig 6.13(a), event-7). Event-8: As expected,
DG3 autonomously and quickly respond to this shortcoming by an accelerated
increase in its contribution in injecting negative-sequence reactive current (Fig 6.13
(a)). Event-9: Finally, at t=0.35s the fourth MSPT constraint happens in DG3 due
to its peak-current limitation. These nine events all happen autonomously without
having any communication between three units. This test case clearly demonstrates
the main contributions of this chapter: 1) the decentralized nature of the proposed
coordination scheme; 2) maximum flexible asymmetrical voltage support of
individual DG units and their cooperative support; 3) intact active power injection
of all DG units during the DOS; 4) effective performance of the proposed DSPM
and MSPT concepts while respecting the important boundary limits.
(a)
(b)
(c)
Test Case B: the proposed DMAS scheme, (a) grid phase-voltages, (b) PCC phase-voltages, (c) positive- and negative sequence voltages of the grid and PCC.
120
(a) (b)
Test Case B: the proposed DMAS scheme: (a) active and positive/negative-sequence reactive currents of DG1, DG2, and DG3, (b) phase-currents of DG1, DG2, and DG3
6.7 Conclusion
This chapter presented a comprehensive coordination control scheme for
maximized and flexible asymmetrical grid support by multiple DG units in an active
distribution network. In addition to being decentralized, the proposed coordination
scheme benefits from three additional features:
1) a maximized flexible asymmetrical voltage support that does not affect
the active power injection of individual units at the time of the support,
2) maximum support point tracking of each unit considering current,
voltage, and power constraints, and
3) wise dynamic support points movement. Furthermore, this chapter
introduced new concepts including allowable flexible support areas and
support points trajectories represented in the negative-reactive-current vs.
121
positive-reactive-current plane. These concepts were applied in the
proposed scheme.
They are also useful for further research in this area. The proposed
comprehensive scheme was tested in the simulated version of a distribution network
in Ontario, Canada. Test results illustrated the superiority of the proposed
techniques compared to the existing methods in the literature.
122
Chapter 7
Conclusion and Future Work
In this chapter, the main findings of the thesis are summarized, and future work
suggestions are presented.
7.1 Thesis Achievements
The achievements of this research project can be summarized as:
1) The available control strategies under asymmetric grid conditions for a
grid-interactive inverter was thoroughly studied.
2) A novel maximum asymmetric support control scheme (i.e., MAS
scheme) was proposed based on the analytical methods. This scheme
enables grid-interactive inverters to use their full potential to flexibly and
optimally support the asymmetric grid voltage.
3) An advanced reference current generation scheme was suggested. This
scheme has multiple objectives such as minimizing the power
oscillations, maximizing the average active or reactive power delivery,
and minimizing asymmetric fault currents.
4) A comprehensive guideline for riding through asymmetric faults and
simultaneously supporting the grid (i.e., ART scheme) is introduced. This
123
scheme enforces large DGs to properly regulate the phase voltages within
the pre-set dynamic limits under short-term asymmetric low voltages.
5) A novel dynamic voltage regulation method is also proposed to accurately
address the ART specifications.
6) A new voltage support scheme with improved accuracy in regulating the
phase voltages at the PCC within the pre-set safety limits was introduced.
This method addresses the drawbacks of the existing approached by
considering the zero-sequence voltage compensation, the output active
power and being adaptive to complex grid impedance (i.e. with resistive
and inductive parts). Two complementary strategies are also augmented
to this method: the adjustable limited active power oscillation and the
maximum active power delivery strategies. These strategies enabled the
proposed voltage support method to have MAS capability.
7) A unique MAS scheme was proposed for multiple GSI units in the parallel
structure which enables the maximum collaboration between the units in
flexible and optimal asymmetric voltage support. This method was called
parallel MAS (PMAS) technique. In addition to ordinary MAS
capabilities, PMAS added the following advantages to the parallel multi-
inverter structure:
a. coordinating the maximum flexible asymmetrical voltage support
and ride-through capabilities of individual units inside the parallel
structure,
b. maximizing the collective dynamic contribution of parallel
structure in boosting the voltage and reducing the
imbalance subject to the constraints of the plant and host system,
c. retaining the active power injection of each inverter unit intact
which leads to power/cost saving in the plant operation as well as
host system stability enhancement, and
124
d. setting different objectives based on the potential requirements in
future grid codes.
8) Another unique MAS scheme was proposed for the autonomous
coordination control of multiple inverters in the distributed structure. This
scheme is named decentralized MAS tracking (DMAS). While achieving
the optimal coordination between the MAS performance of each inverter,
the DMAS eliminates the dependency of the control system to
communication infrastructure. The DMAS scheme is realized using two
core concepts:
a. The maximum support areas were introduced in the positive
negative reactive currents plane.
b. The dynamic support points movement were proposed by two
autonomous strategies.
7.2 Future Works
The proposed control and regulatory schemes (i.e., ART, MAS, PMAS, and
DMAS) can be examined and applied in different applications such as different
types of converter-interfaced DG units, grid-interactive converter-interfaced
microgrids, interlinking converters inside hybrid AC/DC microgrids, and modular
multi-level converter-based HVDC systems. They can be further explored for
various type of energy resources such as permanent magnet synchronous generator-
based wind turbines or converter-based photovoltaic systems, squirrel cage
induction generators, and doubly-fed induction generators. Further investigation is
required for the application of the proposed schemes for micro-units, such as small
roof-top solar panels and electric vehicles. Since the voltage support in most cases
is obtained using the reactive current, the nature of the energy source (that
is responsible for generating the active power) does not affect the effectiveness of
the proposed schemes in theory. However, further study is needed to validate this.
Also, the algorithms can be extended to utilize the active current component in the
supportive techniques. The specification on the active power limitation during the
125
fault and its restoration after the fault is an important area which needs similar
comparative research. These specifications vary in different grid codes based on
system characteristics such as grid strength. Although the imposed specifications
on active power restoration by different grid codes can be adopted by the proposed
supportive and regulation schemes, it is an interesting area for future research on
specific requirements of active power restoration (from the system operator point
of view) under unbalanced grid faults.
7.3 Expected Significance
This research intends to identify the critical challenges of emerging grid-interactive
smart inverters under asymmetric grid conditions. Some of the most significant
benefits of this project are as follows: (1) tackling the reliability challenges brought
by the increasing integration of distributed inverters into the existing power grids,
(2) enforcing large DGs and microgrids to provide maximum support to the grid
under abnormal conditions to guarantee the stable operation of the host system, (3)
applying the advanced control schemes in different configuration (i.e., parallel- and
distributed structures), and in various application, i.e., a single DG system, hybrid
ac/dc microgrids, and active distribution networks, (4) facilitating the booming
growth of high renewable and clean energies integration.
126
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